QAs

Future value

1 (a) You are 20 years old and are considering putting $100 into an account paying 8% per year. How much will you have in the account at age 65 – after 45 years? How much of it will be simple interest, and how much compounded interest?

b) If you could find an account paying 9% per year, how much will you have in the account at age 65?

2. In 1626 Peter Minuit purchased Manhattan Island from the Indians for about $24 worth of trinkets. If the Indians had taken cash instead and invested it to earn 6% per year compounded annually, how much would the Indians have had in 1986, 360 years later?

Present value

3.You plan to marry in 2 years. The expected cost is $10,000 (austere budget). Your parents want to fund the entire cost today. How much should they deposit in bank today if the bank pays interest of 8% per year?

III. FUTURE VALUE/PRESENT VALUE 4. You have the opportunity to buy a piece of land for $10,000. You are sure that 5 years from now it will be worth $20,000. If you can earn 8% per year by investing your money in the bank, is this investment worthwhile?

Decision Rule 1: Choose the investment alternative with the highest future value.

Decision Rule 2: Choose the investment alternative with the highest rate of return.

Decision Rule 3: Choose the investment alternative with the fastest payback.

IV. FV OF AN ANNUITY  A. Ordinary Annuity 5. If you deposit $100 each year into an account starting a year from today for 3 years, how much will you have in the account if you receive 10% interest per year?

B. Annuity due 6. Suppose the first of your 3 deposits into an account paying 10% interest starts today. How much will you have in the account after 3 years?

V. PRESENT VALUE OF AN ANNUITY A. Ordinary annuity 7. Find the PV of three annual payments of $100 into an account that yield 10% per year. The first payment is at the end of the year.

B. Annuity due 8. If in the previous problem the first of 3 payments start today, what will be the PV?

VI. MISCELLANEOUS ANNUITY PROBLEMS 9.Suppose you are 19 years old and want to set aside $876 a year starting one year from today. At a given age you want to start receiving payments of $6,000 per year, and you want to be able to continue receiving the $6,000 for 25 years. If the interest rate is 8%, until what age do you need to contribute the $876 per year?

10.(a) Suppose you are 30 years old and expect to retire when you are 65 years old (after 35 years). Your life expectancy is 80 years (15 years after retirement). Your earnings in constant dollars (real terms) will be $40,000. If real interest rate is 3%, then find the present value of your earnings over 35 years.

(b) From now until the end of your life we have 50 years. Find how much you can spend in each of these 50 years.

(c) How much can you save during each year of your working life of 35 years?

VII. Perpetuity 11.How much do you need to invest in a bank today that will pay you $1000 forever starting 2 years from now? Interest rate is 10% per year?

VIII. UNEVEN CASH FLOWS 12.Calculate the PV of the following variable cash flows: $400 a year from now, $600 two years from now, $800 a year for 11 years starting 3 years from now. Assume interest rate is 9% per year.

13.Mary gets $2,000 from you after one year, $3,000 after 2 years, and $4,000 after 3 years. You want to restructure the loan and pay 3 equal amounts. If interest rate is 10%, how much will be the equal payments?

X.EFFECTIVE ANNUAL RATE 14.You take out a loan at an APR of 12% with monthly compounding,. What is the effective annual rate on your loan?

15.Find the FV of $1,000 after 5 years at 12% annual interest rate compounded monthly.

X. AMORTIZATION 16. You borrow $1,000 today at 10% annual interest and promise to pay back in three annual installments starting one year from today. What would be the yearly payments?

 Loan Amortization Schedule

Year Beg Bal Payment Interest Principal Repayment Ending Bal

1 $1,000.00 $402.11 $100.00 $302.11 $697.89

2 697.89 402.11 69.79 332.32 364.57

3 365.57 402.13* 36.56 365.57 0.00

* Higher payment to force ending balance to zero.

17. You need to borrow $100,000 to buy a house. One bank offers you a mortgage loan to be repaid over 25 years in 300 monthly payments. (a) If the interest rate is 12% per year, what is the amount of the monthly payment?

(b) What would be the remaining balance, total interest payments and principal payments after 10 years?

(c) Another bank offers you a 15-year mortgage loan with a monthly payment of $1,100. Which loan is better?

XI. CONTINUOUS COMPOUNDING 18. Bank A offers 10.5% interest compounded twice a year. Bank B offers 10% interest compounded continuously. In which bank would you deposit your money?