# Future value tables

1) Future value tables

Use the future value interest factors in Appendix Table A 1 in each of the cases shown in the following table to estimate, to the nearest year, how long it would take an initial deposit, assuming no withdrawals, a. To double. b. To quadruple.

Case Interest rate A 7% B 40 C 20 D 10

2) Time value As part of your financial planning, you wish to purchase a new car exactly 5 years from today. The car you wish to purchase costs $ 14,000 today, and your research indicates that its price will increase by 2% to 4% per year over the next 5 years. a. Estimate the price of the car at the end of 5 years if inflation is ( 1) 2% per year and ( 2) 4% per year. b. How much more expensive will the car be if the rate of inflation is 4% rather than 2%?

3) Time value You can deposit $ 10,000 into an account paying 9% annual interest either today or exactly 10 years from today. How much better off will you be at the end of 40 years if you decide to make the initial deposit today rather than 10 years from today?

4) Single- payment loan repayment A person borrows $ 200 to be repaid in 8 years with 14% annually compounded interest. The loan may be repaid at the end of any earlier year with no prepayment penalty. a. What amount will be due if the loan is repaid at the end of year 1? b. What is the repayment at the end of year 4? c. What amount is due at the end of the eighth year?

6) Present value concept Answer each of the following questions. a. What single investment made today, earning 12% annual interest, will be worth $ 6,000 at the end of 6 years? b. What is the present value of $ 6,000 to be received at the end of 6 years if the discount rate is 12%? c. What is the most you would pay today for a promise to repay you $ 6,000 at the end of 6 years if your opportunity cost is 12%? d. Compare, contrast, and discuss your findings in parts a through c.

7) Time value An Iowa state savings bond can be converted to $ 100 at maturity 6 years from purchase. If the state bonds are to be competitive with U. S. savings bonds, which pay 8% annual interest ( compounded annually), at what price must the state sell its bonds? Assume no cash payments on savings bonds prior to redemption.

10) Time value Annuities Marian Kirk wishes to select the better of two 10- year annuities, C and D. Annuity C is an ordinary annuity of $ 2,500 per year for 10 years. Annuity D is an annuity due of $ 2,200 per year for 10 years. a. Find the future value of both annuities at the end of year 10, assuming that Marian can earn ( 1) 10% annual interest and ( 2) 20% annual interest. b. Use your findings in part a to indicate which annuity has the greater future value at the end of year 10 for both the ( 1) 10% and ( 2) 20% interest rates. c. Find the present value of both annuities, assuming that Marian can earn ( 1) 10% annual interest and ( 2) 20% annual interest. d. Use your findings in part c to indicate which annuity has the greater present value for both ( 1) 10% and ( 2) 20% interest rates. e. Briefly compare, contrast, and explain any differences between your findings using the 10% and 20% interest rates in parts b and d.

11) Value of a retirement annuity An insurance agent is trying to sell you an immediate-retirement annuity, which for a single amount paid today will provide you with $ 12,000 at the end of each year for the next 25 years. You currently earn 9% on low- risk investments comparable to the retirement annuity. Ignoring taxes, what is the most you would pay for this annuity?

14) Changing compounding frequency Using annual, semiannual, and quarterly com-pounding periods, for each of the following, ( 1) calculate the future value if $ 5,000 is deposited initially, and ( 2) determine the effective annual rate ( EAR). a. At 12% annual interest for 5 years. b. At 16% annual interest for 6 years. c. At 20% annual interest for 10 years.

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#### Solution Summary

Future value tables are scrutinized.

Managerial Finance: future value of annuity, present value of a security, cash flows

4.1 If you deposit $10,000 in a bank account that pays 10% interest annually, how much will be in your account after 5 years?

4.2 What is the present value of a security that will pay $5,000 in 20 years if securities of equal risk pay 7% annually?

4.6 What is the future value of a 7%, 5-year ordinary annuity that pays $300 each year? If this were an annuity due, what would its future value be?

4.13 Find the present value of the following ordinary annuities

A. $400 per year for 10 years at 10%

B. $200 per year for 5 years at 5%

C. $400 per year for 5 years at 0%

D. Now rework parts a, b, and c assuming that payments are made at the beginning of each year; that is, they are annuities due.

4.14 Find the present values of the following cash flow streams. The appropriate interest rate is 8%

Year Cash Stream A Cash Stream B

1 $100 $300

2 400 400

3 400 400

4 400 400

5 300 100

B. What is the value of each cash flow stream at a 0% interest rate?

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