Question

1. What is the time value of money? Why should accountants have an understanding of compound interest, annuities, and present value concepts?

2. Identify three situations in which accounting measures are based on present values. Do these present value applications involve single sums or annuities, or both single sums and annuities? Explain.

3. What is the nature of interest? Distinguish between “simple interest” and “compound interest.”

4. Jose Oliva is considering two investment options for a $1,500 gift he received for graduation. Both investments have 8% annual interest rates. One offers quarterly compounding; the other compounds on a semiannual basis. Which investment should he choose? Why?

Answer 1

1. A dollar received toady is worth more than a dollar promised at some time in the future. Why? Because the opportunity to invest today's dollar and receive interest on the investment. It is essential to be able to compare today's dollar and tomorrow's dollar on the same footing. Investors do that by using the concept of present value. [The cost or earning of money as a function of time is the time value of money] Compound interest uses the accumulate balance (principal plus interest to date) at each year end to compute interest in the succeeding year. It is the return on principal for two or more time periods. The present value of an annuity is the single sum that, if invested at compound interest now, would provide for an annuity (a series of withdrawals) for a certain number of future periods. The present value of an ordinary annuity is the present value of a series of equal rents, to be withdrawn at equal intervals at the end of the period.
2. 1. computing the unknown present value of a known single sum of money in the future that is discounted for a certain number of periods at a certain interest rate.
   2. Present value of an ordinary annuity: PV of a series of equal rents, to be withdrawn at equal intervals at the end of the period
   3. Present value of an annuity due
3. Interest is the payment for the use of money. It is the excess cash received or repaid over and above the amount lent or borrowed.
   Simple interest is computed on the amount of the principal only, while compound interest is computed on the amount of the principal plus any accumulated interest. Compound interest involves interest on interest while simple interest does not.

4. quartely compounding

r = interest rate = 8%/4= 2% , n = number of term = 4 , pv = present value = 1500

future value = 1500( 1+0.02)^4 =1500 * 1.0824 = $1623.6

for semiannually compunding

r = interest rate = 8%/2= 4% , n = number of term = 2 , pv = present value = 1500

future value = 1500(1+0.04)^2 = 1500 * 1.0816 = $1622.4

he should choose quarterly compounding option as it earn slightly better rate than semiannual compounding