Accounting

1. Three years ago, Caroline invested $7,500. She has earned and will earn compound interest of 3.2 percent per year. In one year from today, Mardy can make an investment and earn simple interest of 13.2 percent per year. If Mardy wants to have as much in 5 years from today as Caroline will have in 5 years from today, then how much should Mardy invest in one year from today?

A. An amount equal to or greater than $6,400 but less than $7,100

B. An amount equal to or greater than $7,100 but less than $7,900

C. An amount equal to or greater than $7,900 but less than $8,600

D. An amount equal to or greater than $8,600 but less than $9,300

E. An amount less than $6,400 or an amount equal to or greater than $9,300

(Fall 2010, test 1, question 6) (Spring 2010, test 1, question 1)

(Fall 2011, test 1, question 1) (Fall 2012, test 1, question 1)

(Fall 2012, final, question 1) (Spring 2014, test 1, question 1)

(Fall 2015, test 1, question 1) (Spring 2016, test 1, question 1)

(Fall 2016, test 1, question 1)

Solve in 2 steps:

1. Compute how much Caroline will have in 5 years

2. Compute how much Mardy needs to invest to have the same amount in 5 years

1. Compute how much Caroline will have in 5 years

With Caroline, C0 = 7,500; r = .032, and t = 8

Note that if she invested 3 years ago, then the money will have 8 years to compound until 5 years from today

So in 5 years from today (8 years after being invested), Caroline will have

C0 × (1+r)t = 7,500 × (1.032)8 = $9,649.37

2. Compute how much Mardy needs to invest to have the same amount in 5 years

With simple interest, an investment of C0 becomes C0 + (C0 × simple interest rate per period × t) in t periods

With Mardy, C0 = ?, simple rate = .132, t = 4, and the amount it will become is 9,649.37

Note that if he invests in 1 year, then the money will have 4 years to change value until 5 years from today

So in 5 years from today, Mardy will have 9,649.37 = [C0 + (C0 × .132 × 4)]

= [C0 + (C0 × .132) + (C0 × .132) + (C0 × .132) + (C0 × .132)]

= [C0 + (C0 × .528)]

= 1.528 × C0

= 9,649.37

So, C0 = 9,649.37 / 1.528 = $6,315.03

Mardy should invest $6,315.03 in 1 year to have as much in 5 years as Caroline will have in 5 years

E. An amount less than $6,400 or an amount equal to or greater than $9,300

2. Two years ago, Rafer invested $1,600. He has earned and will earn compound interest of 8.50 percent per year. If Lainie invests $1,700 in 1 year from today and earns simple interest, then how much simple interest per year must Lainie earn to have the same amount of money in 6 years from today as Rafer will have in 6 years from today? Answer as an annual rate.

A. A rate less than 7.00 percent or an amount equal to or greater than 17.00 percent

B. A rate equal to or greater than 7.00 percent but less than 9.50 percent

C. A rate equal to or greater than 9.50 percent but less than 12.00 percent

D. A rate equal to or greater than 12.00 percent but less than 14.50 percent

E. A rate equal to or greater than 14.50 percent but less than 17.00 percent

(Fall 2009, test 1, question 1) (Spring 2011, test 1, question 2)

(Spring 2012, test 1, question 1) (Spring 2013, test 1, question 2)

(Fall 2013, test 1, question 1) (Fall 2014, test 1, question 1)

(Spring 2015, test 1, question 1) (Fall 2015, final, question 1)

(Spring 2017, test 1, question 1) (Fall 2017, test 1, question 1)

(Spring 2018, test 1, question 1)

Solve in 2 steps:

1. Compute how much Rafer will have in 6 years

2. Compute the simple interest rate needed by Lainie to have the same amount as Rafer in 6 years

1. Compute how much Rafer will have in 6 years

If Rafer invested $1,600 2 years ago, then he will have his money invested for 6 – (2) = 8 years

8 years after investing, Rafer will have C0 × (1+r)t = 1,600 × (1.0850)8 = $3,072.97

2. Compute the simple interest rate needed by Lainie to have the same amount as Rafer in 6 years

With simple interest, an investment of C0 becomes

C0 + (C0 × simple interest rate per period × t) in t periods

If Lainie invests $1,700 in 1 year, then she will have her money invested for 6 – 1 = 5 years

So 3,072.97 = 1,700 + (1,700 × simple interest rate per period × 5)

So 3,072.97 – 1,700 = 1,372.97 = (1,700 × simple interest rate per period × 5)

So 1,372.97 / (1,700 × 5) = 1,372.97 / 8,500 = .1615 = 16.15% = simple interest rate per period

If Lainie invests $1,700 in 1 year and earns simple interest of 16.15% per year, she would have the same amount in 6 years as Rafer, who invested $1,600 two years ago for 8 years at 8.50 percent compound interest. Answers may differ slightly due to rounding.

Answer: E, 16.15% is a rate equal to or greater than 14.50 percent but less than 17.00 percent

Alternatively:

If Lainie invests $1,700 in 1 year, and she wants to have $3,072.97 in 6 years, then she will have her money invested for 6 – 1 = 5 years and will need to earn total simple interest of $3,072.97 – $1,700 = $1,372.97 over the 5 years that her money is invested

To earn $1,372.97 in simple interest over 5 years, she needs to earn [$1,372.97 / 5] = $274.59 in interest per year, since the same amount of interest is earned each year with simple interest

The simple interest rate would be equal to the interest earned per year divided by the initial amount of the investment = [$274.59 / $1,700] = 0.1615 = 16.15% per year

3. For each of the 4 investments described in the table, the investor would pay $500 today to purchase the investment. Each investment would have the annual return noted in the table and each investment would make a single, lump sum payment to the investor in the number of years from today noted in the table. If RA > RB and TQ > TZ, then which assertion is true? All annual returns and numbers of years from today when the single, lump sum payment will be made are greater than zero.

A. Investment A will make a larger single, lump sum payment in T years than investment B will make in T years, and investment Q will make a larger single, lump sum payment in TQ years than investment Z will make in TZ years

B. Investment A will make a larger single, lump sum payment in T years than investment B will make in T years, and investment Z will make a larger single, lump sum payment in TZ years than investment Q will make in TQ years

C. Investment B will make a larger single, lump sum payment in T years than investment A will make in T years, and investment Q will make a larger single, lump sum payment in TQ years than investment Z will make in TZ years

D. Investment B will make a larger single, lump sum payment in T years than investment A will make in T years, and investment Z will make a larger single, lump sum payment in TZ years than investment Q will make in TQ years

(Spring 2011, test 1, question 1)

(Fall 2011, final, question 1)

(Spring 2013, test 1, question 1)

(Fall 2014, final, question 1)

(Fall 2017, test 1, question 2)

Investment A will make a larger single, lump sum payment in T years than investment B

With any investment in T years, you would have 500 × (1 + r)T

With investment A, you would have 500 × (1 + RA)T in T years

With investment B, you would have 500 × (1 + RB)T in T years

We can conclude that 500 × (1 + RA)T > 500 × (1 + RB)T

Since both A and B are positive, 1+RA and 1+RB are both greater than 1, which means that both investments get more valuable each year, and since RA > RB, investment A will get more valuable each year than investment B

Investment Q will make a larger single, lump sum payment in TQ years than investment Z will make in TZ years

With any investment with a return of R per year, you would get 500 × (1 + R)t in t years

With investment Q, you would get 500 × (1 + R)TQ in TQ years

With investment Z, you would get 500 × (1 + R)TZ in TZ years

We can conclude that 500 × (1 + R)TQ > 500 × (1 + R)TZ

Since R is positive, 1+R is greater than 1, which means that both investments get more valuable each year, and since TQ > TZ, investment Q will increase its value for more years, so it will pay a larger single, lump sum than investment Z, which will pay off earlier

Putting it together, the answer is:

A. Investment A will make a larger single, lump sum payment in T years than investment B and investment Q will make a larger single, lump sum payment in TQ years than investment Z will make in TZ years

4. Which assertion is true?

A. Albert will have more money in 10 years than Brooke will have in 10 years and Albert will have more money in 10 years than Cassius will have in 10 years

B. Albert will have more money in 10 years than Brooke will have in 10 years and Cassius will have more money in 10 years than Albert will have in 10 years

C. Brooke will have more money in 10 years than Albert will have in 10 years and Albert will have more money in 10 years than Cassius will have in 10 years

D. Brooke will have more money in 10 years than Albert will have in 10 years and Cassius will have more money in 10 years than Albert will have in 10 years

(Fall 2010, test 1, question 1 – simpler version on exam than in test bank)

(Spring 2018, test 1, question 2)

To answer this question, we need to compare the future values as of 10 years from today.

Albert: r = .0882; t = 10; k = 0; t – k = 10 – 0 = 10; C0 = 11,200

FV10 = Ck × (1+r)t-k = 11,200 × (1.0882)10 = 26,080

Mode is not relevant, since PMT = 0

Enter 10 8.82 -11,200 0

N I% PV PMT FV

Solve for 26,080

Brooke: r = .0924; t = 10; k = 7; t – k = 10 – 7 = 3; C7 = 18,900

FV10 = Ck × (1+r)t-k = 18,900 × (1.0924)3 = 24,638

Mode is not relevant, since PMT = 0

Enter 3 9.24 -18,900 0

N I% PV PMT FV

Solve for 24,638

In 10 years, Albert will have $26,080 and Brooke will have $24,638

Albert will have more money than Brooke

Cassius: r = .0826; t = 10; k = 4; t – k = 10 – 4 = 6; C4 = 16,300

FV10 = Ck × (1+r)t-k = 16,300 × (1.0826)6 = 26,242

Mode is not relevant, since PMT = 0

Enter 6 8.26 -16,300 0

N I% PV PMT FV

Solve for 26,242

In 10 years, Albert will have $26,080 and Cassius will have $26,242

Cassius will have more money than Albert

Putting it all together: B. Albert will have more money in 10 years than Brooke will have in 10 years and Cassius will have more money in 10 years than Albert will have in 10 years

5. What is X if X equals the value of investment A plus the value of investment B? Investment A is expected to pay $26,000 in 5 years from today and has an expected return of 14.19 percent per year. Investment B is expected to pay $37,000 in 9 years from today and has an expected return of 8.72 percent per year.

Value of investment A

PV0 = Ct ÷ (1+r)t

For A, r = .1419; t = 5; C5 = 26,000

PV0 = Ct ÷ (1+r)t = C5 ÷ (1+r)5 = 26,000 ÷ (1.1419)5 = 13,392

Mode is not relevant, since PMT = 0

Enter 5 14.19 0 26,000

N I% PV PMT FV

Solve for -13,392

The value of investment A is $13,392

Value of investment B

PV0 = Ct ÷ (1+r)t

For B, r = .0872; t = 9; C9 = 37,000

PV0 = Ct ÷ (1+r)t = C9 ÷ (1+r)9 = 37,000 ÷ (1.0872)9 = 17,435

Mode is not relevant, since PMT = 0

Enter 9 8.72 0 37,000

N I% PV PMT FV

Solve for -17,435

The value of investment B is $17,435

Find X

X = value of investment A + value of investment B

Value of investment A is $13,392

Value of investment B is $17,435

X = $13,392 + $17,435 = $30,827

6. Fairfax Cookie just bought 2 tons of chocolate chips from Chantilly Chocolate. Fairfax Cookie has been offered the 3 possible payment options described in the table. If the discount rate is 9.0%, which of the assertions is true?

A. Fairfax Cookie should prefer option A more than option B, and Fairfax Cookie should prefer option A more than option C

C. Fairfax Cookie should prefer option B more than option A, and Fairfax Cookie should prefer option A more than option C

D. Fairfax Cookie should prefer option B more than option A and Fairfax Cookie should prefer option C more than option A

(Fall 2009, test 1, question 9)

(Spring 2010, test 1, question 3)

To answer this question, we need to find the present value of options B and C and compare them to option A because a firm would be indifferent between paying Ct in t years and paying an amount equal to the present value of Ct today, prefer to pay an amount today that is less than the present value of Ct more than it would prefer to pay Ct in t years, and prefer to pay Ct in t years more than it would prefer to pay an amount today that is greater than the present value of Ct.

Option A involves paying 10,000 today, which is a cash flow of -$10,000

PV0 = Ct ÷ (1+r)t

Option B: r = .090; t = 2; C2 = -12,000

PV0 = Ct ÷ (1+r)t = C2 ÷ (1+r)2 = -12,000 ÷ (1.090)2 = -10,100

Mode is not relevant, since PMT = 0

Enter 2 9.0 0 -12,000

N I% PV PMT FV

Solve for 10,100

The present value of option B is -10,100, which is greater in magnitude than -$10,000, the payment associated with A, so Fairfax Cookie should prefer option A more than option B

Option C: r = .090; t = 4; C4 = -14,000

PV0 = Ct ÷ (1+r)t = C4 ÷ (1+r)4 = -14,000 ÷ (1.090)4 = -9,918

Mode is not relevant, since PMT = 0

Enter 4 9.0 0 -14,000

N I% PV PMT FV

Solve for 9,918

The present value of option C is -9,918, which is smaller in magnitude than -$10,000, the payment associated with A, so Fairfax Cookie should prefer option C more than option A

Putting it all together:

B. Fairfax Cookie should prefer option A more than option B and Fairfax Cookie should prefer option C more than option A

7. Euro Gyro just bought 50 cases of pita bread from Supply House. Euro Gyro has been offered the 3 possible payment options described in the table. If the discount rate is 14.3%, which of the assertions is true?

A. Supply House should prefer option A more than option B, and Supply House should prefer option A more than option C

B. Supply House should prefer option A more than option B, and Supply House should prefer option C more than option A

C. Supply House should prefer option B more than option A, and Supply House should prefer option A more than option C

D. Supply House should prefer option B more than option A, and Supply House should prefer option C more than option A

(Fall 2011, test 1, question 2) (Fall 2012, test 1, question 4)

(Fall 2013, test 1, question 3) (Spring 2015, test 1, question 2)

To answer this question, we need to find the present values of options A, B, and C and compare the present values of options B & C to that of option A. The higher present value is preferred. Since the alternatives involve payment from Euro Gyro to Supply House, present values for Supply House are positive, so higher present value involves a greater magnitude.

Option A: r = .143; t = 1; C1 = 6,300

PV0 = Ct ÷ (1+r)t = C1 ÷ (1+r)1 = 6,300 ÷ (1.143)1 = 5,512

Mode is not relevant, since PMT = 0

Enter 1 14.3 0 6,300

N I% PV PMT FV

Solve for -5,512

Present value of option A = $5,512

Option B: r = .143; t = 3; C3 = 8,100

PV0 = Ct ÷ (1+r)t = C3 ÷ (1+r)3 = 8,100 ÷ (1.143)3 = 5,424

Mode is not relevant, since PMT = 0

Enter 3 14.3 0 8,100

N I% PV PMT FV

Solve for -5,424

Present value of option B = $5,424

The present value of option A is $5,512, which is greater than the present value of option B, which is $5,424, so Supply House should prefer option A more than option B

Option C: r = .143; t = 5; C4 = 10,700

PV0 = Ct ÷ (1+r)t = C5 ÷ (1+r)5 = 10,700 ÷ (1.143)5 = 5,485

Mode is not relevant, since PMT = 0

Enter 5 14.3 0 10,700

N I% PV PMT FV

Solve for -5,485

Present value of option C = $5,485

The present value of option A is $5,512, which is greater than the present value of option C, which is $5,485, so Supply House should prefer option A more than option C

Putting it all together: A. Supply House should prefer option A more than option B and Supply House should prefer option A more than option C

8. Danielle owns two investments, A and B, that have a combined total value of $25,000. Investment A is expected to pay $24,800 in 4 years from today and has an expected return of 12.79 percent per year. Investment B is expected to pay X in 7 years from today and has an expected return of 8.22 percent per year. What is X, the cash flow expected from investment B in 7 years from today?

(Fall 2012, test 1, question 3)

(Fall 2015, test 1, question 2)

To solve:

1) Find the value of investment A

2) Find the value of investment B as the combined value of both A and B minus the value of A

3) Find X, the cash flow expected from investment B in 7 years

1) Find the value of investment A

PV0 = Ct / (1+r)t

Ct = 24,800

r = .1279

t = 4

PV0 = C4 / (1+r)4

= 24,800 / (1.1279)4

= $15,324

Mode is not relevant since PMT = 0

Enter 4 12.79 0 24,800

N I% PV PMT FV

Solve for -15,324

Investment A is worth $15,324

2) Find the value of investment B as the value of both A and B minus the value of A

Value of B = value of A and B – value of A

Value of A and B = $25,000

Value of A = $15,324

Value of B = $25,000 – $15,324 = $9,676

3) Find X, the cash flow expected from investment B in 7 years

PV0 = Ct / (1+r)t

Ct = X

r = .0822

t = 7

PV0 = 9,676

So 9,676 = X / (1.0822)7

So X = 9,676 × (1.0822)7

= 16,821

Mode is not relevant since PMT = 0

Enter 7 8.22 -9,676 0

N I% PV PMT FV

Solve for 16,821

Investment B is expected to pay $16,821 in 7 years

9. Cowboy Frozen Custard is planning to sell its Dallas, Houston, and San Antonio stores in S years from today. The firm expects to sell its Dallas store for a cash flow of $A, its Houston store for a cash flow of $A, and its San Antonio store for a cash flow of $B. The cost of capital for the Dallas store is Y percent, the cost of capital for the San Antonio store is Y percent, the cost of capital for the Houston store is X percent, A > B > 0, Y > X > 0, and S > 0. The cash flows from the sales are the only cash flows associated with the various stores. Based on the information in the preceding paragraph, which of the stores is most valuable?

A. The Dallas store is the most valuable of the 3 stores

B. The Houston store is the most valuable of the 3 stores

C. The San Antonio store is the most valuable of the 3 stores

D. Two of the three stores have equal value and those two stores are more valuable than the third store or all three stores have the same value

E. None of the above assertions is true

(Spring 2011, final, question 1)

(Fall 2012, test 1, question 5)

(Spring 2016, test 1, question 2)

1. We know that the Houston store is more valuable than the Dallas store, since they both are expected to produce the same cash flow of $A in S years, but the Houston store has a lower discount rate, since Y > X.

A/(1+X)S > A/(1+Y)S

2. We know that the Dallas store is more valuable than the San Antonio store, since they both are expected to produce cash flows at the same time in S years and have the same discount rate of Y percent, but the Dallas store is expected to be sold for more money than the San Antonio store and therefore produce a higher cash flow in S years, since A > B.

A/(1+Y)S > B/(1+Y)S

Putting it all together: the Houston store is more valuable than the Dallas store, which is more valuable than the San Antonio store.

Answer: B. The Houston store is the most valuable of the 3 stores

10. Florida Fashion is planning to sell its Miami, Tampa, and Orlando stores. The firm expects to sell each of the three stores for the same, positive cash flow of $A. The firm expects to sell its Tampa store in S years, its Orlando store in S years, and its Miami store in T years. The cost of capital for the Tampa store is Y percent, the cost of capital for the Miami store is Y percent, the cost of capital for the Orlando store is X percent, T > S > 0, and Y > X > 0. The cash flows from the sales are the only cash flows associated with the various stores. Based on the information in the preceding paragraph, which one of the following assertions is true?

A. The Tampa store is the most valuable of the 3 stores

B. The Miami store is the most valuable of the 3 stores

C. The Orlando store is the most valuable of the 3 stores

D. Two of the three stores have equal value and those two stores are more valuable than the third store or all three stores have the same value

E. None of the above assertions is true

(Fall 2010, test 1, question 5)

(Fall 2011, test 1, question 6)

(Fall 2013, test 1, question 4)

(Spring 2014, final, question 1)

1. We know that the Orlando store is more valuable than the Tampa store, since they both are expected to produce the same cash flow of $A in S years, but the Orlando store has a lower discount rate, since Y > X.

A/(1+X)S > A/(1+Y)S

2. We know that the Tampa store is more valuable than the Miami store, since they both are expected to produce the same cash flow of $A and have the same discount rate of Y percent, but the Miami store is expected to be sold later than the Tampa store, since T > S. We know that if all else is equal (amount of cash flow and discount rate), then cash flows that are received sooner have more value than those received later.

A/(1+Y)S > A/(1+Y)T

Putting it all together: the Orlando store is more valuable than the Tampa store, which is more valuable than the Miami store.

Answer: C. The Orlando store is the most valuable of the 3 stores

11. East Coast Athletics is planning to sell its Wilmington, Philadelphia, and Boston gyms. The firm expects to sell its Wilmington gym for a cash flow of $A, its Philadelphia gym for a cash flow of $A, and its Boston gym for a cash flow of $B. The firm expects to sell its Wilmington gym in T years, its Philadelphia gym in S years, and its Boston gym in S years. The cost of capital for all three gyms is Y, B > A > 0, T > S > 0, and Y > 0. The cash flows from the sales are the only cash flows associated with the various gyms. Based on the information in the preceding paragraph, which one of the following assertions is true?

A. The Philadelphia gym is the most valuable of the 3 gyms

B. The Wilmington gym is the most valuable of the 3 gyms

C. The Boston gym is the most valuable of the 3 gyms

D. Two of the three gyms have equal value and those two gyms are more valuable than the third gym or all three gyms have the same value

E. None of the above assertions is true

(Fall 2009, test 1, question 3 – exam question is simpler than test bank problem)

(Spring 2012, test 1, question 3)

(Fall 2013, final, question 1)

(Spring 2017, test 1, question 2)

1. We know that the Philadelphia gym is more valuable than the Wilmington gym, since they both are expected to produce the same cash flow of $A and have the same discount rate of Y, but the Philadelphia gym is expected to be sold sooner and produce that cash flow earlier, since T > S.

A/(1+Y)S > A/(1+Y)T

2. We know that the Boston gym is more valuable than the Philadelphia gym, since they both are expected to produce cash flows at the same time in S years and have the same discount rate of Y percent, but the Boston gym is expected to be sold for more money than the Philadelphia gym and therefore produce a higher cash flow in S years, since B > A.

B/(1+Y)S > A/(1+Y)S

Putting it all together: the Boston gym is more valuable than the Philadelphia gym, which is more valuable than the Wilmington gym.

Answer: C. The Boston gym is the most valuable of the 3 gyms

12. Based on the information in the table, which one of the assertions is true?

A. Investment A is more valuable than investment B and investment C is riskier than investment D

B. Investment A is more valuable than investment B and investment D is riskier than investment C

C. Investment B is more valuable than investment A and investment C is riskier than investment D

D. Investment B is more valuable than investment A and investment D is riskier than investment C

(Spring 2013, test 1, question 3)

(Spring 2014, test 1, question 3)

(Spring 2015, final, question 1)

(Fall 2015, final, question 2)

Compare A and B

A: PV0 = Ct ÷ (1+r)t = 6,800 / (1.1670)3 = $4,278.55

Mode is not relevant, since PMT = 0

Enter 3 16.70 0 6,800

N I% PV PMT FV

Solve for -4,278.55

B: PV0 = Ct ÷ (1+r)t = 8,100 / (1.1340)5 = $4,319.36

Mode is not relevant, since PMT = 0

Enter 5 13.40 0 8,100

N I% PV PMT FV

Solve for -4,319.36

B is more valuable than A, because B has a higher present value than A

Compare C and D

C: Mode is not relevant, since PMT = 0

Enter 6 -2,300 0 3,800

N I% PV PMT FV

Solve for 8.73

D: Mode is not relevant, since PMT = 0

Enter 8 -2,900 0 5,600

N I% PV PMT FV

Solve for 8.57

C is riskier than D, because C has a higher expected return than D

Put it together

Answer: C. Investment B is more valuable than investment A and investment C is riskier than investment D 13. Felicity owns two investments, A and B, that have a combined total value of $28,000. Investment A is expected to pay $25,000 in 4 years from today and has an expected return of 12.74 percent per year. Investment B is expected to pay $21,400 in 6 years from today and has an expected return of R per year. What is R, the expected annual return for investment B?

(Fall 2009, test 1, question 7 – exam question is simpler than test bank problem)

(Fall 2016, test 1, question 2)

To solve:

1) Find the value of investment A

2) Find the value of investment B as the combined value of both A and B minus the value of A

3) Find R, the expected return for investment B

1) Find the value of investment A

PV0 = Ct / (1+r)t

Ct = 25,000

r = .1274

t = 4

PV0 = C4 / (1+r)4

= 25,000 / (1.1274)4

= $15,475

Mode is not relevant since PMT = 0

Enter 4 12.74 0 25,000

N I% PV PMT FV

Solve for -15,475

Investment A is worth $15,475

2) Find the value of investment B as the value of both A and B minus the value of A

Value of B = value of A and B – value of A

Value of A and B = $28,000

Value of A = $15,475

Value of B = $28,000 – $15,475 = $12,525

3) Find R, the expected return for investment B

Mode is not relevant since PMT = 0

Enter 6 -12,525 0 21,400

N I% PV PMT FV

Solve for 9.34

Investment B has an expected return of 9.34 percent

14. Alicia owns two investments, A and B, that have a combined total value of $31,300. Investment A is expected to pay $24,800 in 4 years from today and has an expected return of 12.72 percent per year. Investment B is expected to pay $27,100 in T years from today and has an expected return of 8.19 percent per year. What is T, the number of years from today that investment B is expected to pay $27,100?

(Fall 2011, test 1, question 3)

(Spring 2012, final, question 1)

(Spring 2016, final, question 1)

(Fall 2017, test 1, question 3)

To solve:

1) Find the value of investment A

2) Find the value of investment B as the combined value of both A and B minus the value of A

3) Find T, the number of years from today that investment B is expected to pay $27,100

1) Find the value of investment A

PV0 = Ct / (1+r)t

Ct = 24,800

r = .1272

t = 4

PV0 = C4 / (1+r)4

= 24,800 / (1.1272)4

= $15,362

Mode is not relevant since PMT = 0

Enter 4 12.72 0 24,800

N I% PV PMT FV

Solve for -15,362

Investment A is worth $15,362

2) Find the value of investment B as the value of both A and B minus the value of A

Value of B = value of A and B – value of A

Value of A and B = $31,300

Value of A = $15,362

Value of B = $31,300 – $15,362 = $15,938

3) Find T, the number of years from today that investment B is expected to pay $27,100

Mode is not relevant since PMT = 0

Enter 8.19 -15,938 0 27,100

N I% PV PMT FV

Solve for 6.74

Investment B is expected to make its payment in 6.74 years

15. Four years ago, Mack invested $6,100. In 1 year from today, he expects to have $9,100. If Mack expects to earn the same annual return after 1 year from today as the annual rate implied from the past and expected values given in the problem, then how much does Mack expect to have in 4 years from today?

(Spring 2010, test 2, question 2) (Fall 2011, test 1, question 5)

(Fall 2013, test 1, question 5) (Spring 2014, final, question 2)

(Spring 2016, test 1, question 3) (Fall 2016, final, question 1)

(Spring 2017, test 1, question 3) (Fall 2017, final, question 1)

To solve:

1) Find the implied return over the 5-year time frame from 4 years ago to 1 year from today

2) Use the implied return to determine future value, making sure to use correct number of years

1) Find the implied return over the 5-year time frame from 4 years ago to 1 year from today

Mode is not relevant, since PMT = 0

Enter 5 -6,100 0 9,100

N I% PV PMT FV

Solve for 8.33

2) Use the implied return to determine future value, making sure to use correct number of years

Note: 4 years from today is 3 years from 1 year from today, when Mack expects to have $9,100

Mode is not relevant, since PMT = 0

Enter 3 8.33 -9,100 0

N I% PV PMT FV

Solve for 11,569

Mack expects to have $11,569 in 4 years from today

Solutions may differ somewhat due to rounding

Alternatively

Note: 4 years from today is 8 years from 4 years ago, when Mack had $6,100

Mode is not relevant, since PMT = 0

Enter 8 8.33 -6,100 0

N I% PV PMT FV

Solve for 11,570

Mack expects to have $11,570 in 4 years from today

(Fall 2010, final, question 1)

(Fall 2014, test 1, question 3)

To solve, use the value of his account from 2 years ago and the expected value in his account in 5 years to find the implied rate. Then, by either of two approaches, use this implied rate to find how much is expected in his account in 1 year from today.

Find the implied rate

Mode is not relevant, since PMT = 0

Enter 7 -152,000 0 396,000

N I% PV PMT FV

Solve for 14.66

Now the account value as of 1 year from today can be found using one of several approaches

1) The value of the account in 1 year from today is the present value of an account that is expected to be worth $396,000 in 5 years from today (which is 4 years later) and has an expected return of 14.66%

Mode is not relevant, since PMT = 0

Enter 4 14.66 0 396,000

N I% PV PMT FV

Solve for -229,112

2) The value of the account in 1 year from today is the future value 3 years later for an account that was worth $152,000 2 years ago and has an expected return of 14.66%

Mode is not relevant, since PMT = 0

Enter 3 14.66 -152,000 0

N I% PV PMT FV

Solve for 229,129

Answers differ slightly with the two approaches due to rounding

(Spring 2010, test 1, question 4) (Fall 2012, test 1, question 6)

(Spring 2013, test 1, question 4) (Spring 2013, final, question 1)

(Fall 2013, final, question 2) (Spring 2014, test 1, question 4)

(Fall 2014, final, question 2) (Spring 2015, test 1, question 3)

(Fall 2015, test 1, question 3) (Fall 2016, test 1, question 3)

(Spring 2017, final, question 1) (Spring 2018, test 1, question 3)

To solve:

1) Find the implied return over the 5-year time frame from 4 years ago to 1 year from today

2) Use the implied return to determine when goal will be reached relative to one of the given values and then relative to today

1) Find the implied return over the 5-year time frame from 4 years ago to 1 year from today

Mode is not relevant, since PMT = 0

Enter 5 -5,900 0 10,200

N I% PV PMT FV

Solve for 11.57

2) Use the implied return to determine when goal will be reached relative to one of the given values and then relative to today

Mode is not relevant, since PMT = 0

Enter 11.57 -10,200 0 17,200

N I% PV PMT FV

Solve for 4.77

Jack would have $17,200 in 4.77 years from 1 year from today

Therefore, Jack would have $17,200 in 5.77 years from today

Solutions may differ somewhat due to rounding

Alternatively

Mode is not relevant, since PMT = 0

Enter 11.57 -5,900 0 17,200

N I% PV PMT FV

Solve for 9.77

Jack would have $17,200 in 9.77 years from 4 years ago

Therefore, Jack would have $17,200 in 5.77 years from today

Solutions may differ somewhat due to rounding

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