FIN HW

1-Compute the present value of a $170 cash flow for the following combinations of discount rates and times: (Do not round intermediate calculations. Round your answers to 2 decimal places.)

    Present Value

  a. r = 10%, t = 9 years

$      

  b. r = 10%, t = 18 years

  c. r = 5%, t = 9 years

  d. r = 5%, t = 18 years

2- Compute the future value of a $160 cash flow for the same combinations of rates and times: (Do not round intermediate calculations. Round your answers to 2 decimal places.)

     Future Value

  a. r = 8%, t = 10 years

$      

  b. r = 8%, t = 20 years

  c. r = 4%, t = 10 years

  d. r = 4%, t = 20 years

3-Find the APR (the stated interest rate) for each case. (Do not round intermediate calculations. Round your answers to 1 decimal place.)

Effective Annual Interest Rate

Compounding Period

APR

13.35

%

1

 month

%  

6.61

6

 months

%  

9.31

3

 months

%  

4- Lenny Loanshark charges “1.15 points” per week (that is, 1.15% per week) on his loans. What APR must he report to consumers? Assume exactly 52 weeks in a year. What is the effective annual rate? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  Effective annual rate

%  

5- You want to buy a new car, but you can make an initial payment of, only $2,700 and can afford monthly payments of at most $575.

a.

If the APR on auto loans is 9% and you finance the purchase over 36 months, what is the maximum price you can pay for the car? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  Maximum price

$  

b.

How much can you afford if you finance the purchase over 48 months? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  Maximum price

$  

6- A- If you borrow $2,100 and agree to repay the loan in four equal annual payments at an interest rate of 10%, what will your payment be? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  Amount of payment

$  

b.

What if you make the first payment on the loan immediately instead of at the end of the first year? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  Repayment amount

$  

7- Home loans typically involve “points,” which are fees charged by the lender. Each point charged means that the borrower must pay 1% of the loan amount as a fee. For example, if the loan is for $160,000 and 3 points are charged, the loan repayment schedule is calculated on a $160,000 loan but the net amount the borrower receives is only $155,200. What is the effective annual interest rate charged on such a loan assuming loan repayment occurs over 168 months? Assume the interest rate is 1.25% per month. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  Effective annual interest rate

%

8- You’ve borrowed $3,122.85 and agreed to pay back the loan with monthly payments of $170. If the interest rate is 15% stated as an APR.

a.

How long will it take you to pay back the loan? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

  Number of months

b.

What is the effective annual rate on the loan? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  Effective annual rate

%  

9- The $16.5 million lottery payment that you just won actually pays $1.1 million per year for 15 years. If the discount rate is 9% and the first payment comes in 1 year.

a.

What is the present value of the winnings? (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.)

  Present value

$ million  

b.

What is the present value of the winnings, if the first payment comes immediately? (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.)

  Present value

$ million  

10- If a bank pays 5.1% interest with continuous compounding, what is the effective annual rate? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  Effective annual rate

%  

11- I now have $25,000 in the bank earning interest of 1.00% per month. I need $35,000 to make a down payment on a house. I can save an additional $100 per month. How long will it take me to accumulate the $35,000? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  Time taken to accumulate

months

12- A local bank will pay you $152 a year for your lifetime if you deposit $1,900 in the bank today. If you plan to live forever, what interest rate is the bank paying? (Round your answer to 2 decimal places.)

  Interest rate

%

13- You can buy property today for $2.5 million and sell it in 4 years for $3.5 million. (You earn no rental income on the property.)

a.

If the interest rate is 8.75%, what is the present value of the sales price? (Do not round intermediate calculations. Enter your answer in millions rounded to 3 decimal places.)

  Present value

$

 million

b.

Is the property investment attractive to you?

c-1.

What is the present value of the sales price, if you also could earn $150,000 per year rent on the property? (Do not round intermediate calculations. Enter your answer in millions rounded to 3 decimal places.)

  Present value

$

 million

c-2.

Is the property investment attractive to you?

14- A factory costs $350,000. You forecast that it will produce cash inflows of $70,000 in year 1, $130,000 in year 2, and $200,000 in year 3. The discount rate is 10%.

a.

Calculate the PV of cash inflows. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  Present value

$  

b.

Is the factory a good investment?

15- You believe you will need to have saved $530,000 by the time you retire in 30 years in order to live comfortably. If the interest rate is 6% per year, how much must you save each year to meet your retirement goal? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  Annual savings

$  

16- You believe you will spend $42,000 a year for 18 years once you retire in 36 years. If the interest rate is 5% per year, how much must you save each year until retirement to meet your retirement goal? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

   Annual savings

$  

17- If investors are to earn a 2.4% real interest rate, what nominal interest rate must they earn if the inflation rate is (Do not round intermediate calculations. Round your answers to 2 decimal places.)

   Nominal    Interest Rate

  a. zero

%    

  b. 3.4%

%    

  c. 5.4%

%