Appendix II – Compound Interest and the Concept of Present Value
App II-1
APPENDIX II
Compound Interest and the Concept of Present
Value
ANSWERS TO REVIEW QUESTIONS
II-2 This formula says that the future value, Fn, is equal to the present value, P, multiplied
II-4 This statement is false. As the discount rate increases, the present value of a future
cash flow decreases. A higher discount rate means a higher return on funds that are
II-5 These two cash flows are economically equivalent in the sense that a $100 cash flow
II-6 An annuity is a series of equally spaced, identical cash flows. For example, a five-
Appendix II – Compound Interest and the Concept of Present Value
App II-2
SOLUTIONS TO EXERCISES
EXERCISE II-7 (25 MINUTES)
1. Use formula (1):
The accumulation factor, (1.14)6, is given in Table I of Appendix A to Chapter 16. It is
2.195. Thus, the calculation is as follows:
2. Use formula (2):
The discount factor, 1/(1.12)5, is given in Table III of Appendix A to Chapter 16. It is
.567. Thus, the calculation is as follows:
3. You need to invest an amount, A, each year so that the following equation is
satisfied:
The number 4.375 is the annuity accumulation factor, from Table II of Appendix A to
Chapter 16, for n = 4 and r = .06. Rearranging the equation above, we solve for A as
follows:
Appendix II – Compound Interest and the Concept of Present Value
App II-3
EXERCISE II-7 (CONTINUED)
4. You need an amount, P, now so that the following equation is satisfied.
EXERCISE II-8 (45 MINUTES)
1. Future value of investment:
Interest, year 1 (.14 x $2,500.00)
350.00
Interest, year 3 (.14 x $3,249.00)
454.86
Interest, year 4 (.14 x $3,703.86)
Interest, year 5 (.14 x $4,222.40)
591.14
Interest, year 6 (.14 x $4,813.54)
Year 3
Amount at time 5
Time 0
Year 1
Amount at time 0
$2,500.00
Appendix II – Compound Interest and the Concept of Present Value
App II-4
EXERCISE II-8 (CONTINUED)
2. Educational expense fund:
Deposit $32,331 ………………………………………….. $32,331
Earn interest ($32,331 x .10) ………………………… 3,233
Time 0
Year 1
Appendix II – Compound Interest and the Concept of Present Value
App II-5
EXERCISE II-9 (20 MINUTES)
1. To determine the amount you need to accumulate by the time you retire, calculate
the present value of a 40-year annuity in the amount of $225,000. (Use Table IV of
Appendix A to Chapter 16.)
2. To determine the amount you need to deposit each year for 15 years, calculate the
annuity amount that will accumulate to a future value of $1,854,900 in 15 years. (Use
Table II of Appendix A to Chapter 16.)
3. This is both a present-value and a future-value problem. The problem has two parts.