You just received a bonus of $2,000.
a. Calculate the future value of $2,000, given that it will be held in the bank for 9 years and earn an annual interest rate of 8
percent?
b. Recalculate part (a) using a compounding period that is (1) semiannual and (2) bimonthly.
c. Recalculate parts (a) and (b) using an annual interest rate of 16 percent.
d. Recalculate part (a) using a time horizon of 18 years at an annual interest rate of 8 percent
.e. What conclusions can you draw when you compare the answers in parts
(c) and (d) with the answers in parts (a) and (b)?
ANSWER
a:
Future value=Present value*(1+Rate)^number of periods
= 2000*(1+8%)^9
=3998.00
b:
Semi-annual
Future value=Present value*(1+Rate)^number of periods
= 2000*(1+8%/2)^(9*2)
=4051.63
Bi-Monthly
Future value=Present value*(1+Rate)^number of periods
= 2000*(1+8%/6)^(9*6)
=4089.36
c:
Recalculate parts (a) and (b) using an annual interest rate of 8 percent.
- Annual Compounding
Future value = 2000*(1.16)^9
= 2000*3.802
= 7605.92
-semiannual
Future value = 2000*(1+(.16/2))^(9*2)
= 6851.89
-bimonthly.
Future value = 2000*(1+(.16/6))^(9*6)
= 8283.63
d:
Recalculate part (a) using a time horizon of 18 years at an annual interest rate of 8 percent.
Future value
= 2000*(1.08)^18
= 2000*3.996019
= 7992.03
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