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Homework answers / question archive / Suppose you receive $100 at the end of each year for the next three years
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? b. What is the future value in three years of the present value you computed in (a)? 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 (1,17
a) Computation of Present Value of Cash Flows:
Present Value of Cash Flows = P*[1-(1/(1+r)^n)]/r
Here,
P = Cash Flows = $100
r = 8%
n = 3 years
Present Value of Cash Flows = $100*[1-(1/(1+8%)^3)]/8% = $257.71
b) Computation of Future Value:
Future Value = Present Value*(1+Rate)^Time
= $257.71*(1+8%)^3
Future Value = $324.64
c)
Year 1
Balance at end = $100
Year 2
Balance at end = $100 * 1.08 (the $100 above would earn interest) + $100 = $208
Year 3
Balance at end = $208 * 1.08 + $100 = $324.64 (same as in B because we are discounting and then compounding with the same interest rate).
