Question

1. Suppose you receive $100 at the end of each year for the next three years. a. If the interest rate is 8%, what is the present value of these cash flows? (Answer: $257) b. What is the future value in three years of the present value you computed in (a)? (Answer: $324.61) c. Suppose you deposit the cash flows in a bank account that pays 8% interest per year. What is the balance in the account at the end of each of the next three years (after your deposit is made)? How does the final bank balance compare with your answer in (b)?

Answer 1

a) Present value = Amount received x PVFA (8%, 3) = $100 x 2.577 = $257.7 or $257

Present value factor annuity (PVFA) is computed as the sum of present value factors (PVF) for all the years. PVF is computed as 1/ (1+r)ⁿ, where r is the interest rate and n is the year. Like for year 1 it would be 1/ (1.08)¹, for year 2 1/ (1.08)² and so on. If you add these individual values for 3 years, you would get the PVFA for 3 years.

b) Future value = Present Value x (1 + r)³ = $257.7 x (1.08)³ = $324.62 (rounding off difference)

c)

Year 1

Balance at end = $100

Year 2

Balance at end = $100 x 1.08 (the $100 above would earn interest) + $100 = $208

Year 3

Balance at end = $208 x 1.08 + $100 = $324.64 (same as in B because we are discounting and then compounding with the same interest rate)