Answer:
a. $27,538
b. $27,608
c. $27,662
d. $54,366
Explanation:
Future value of the investment is the sum of principal value and interest value including its compounding effect.
Use following formula of FV to calculate the Value of Investment.
FV = PV x ( 1 + r )^n
As per given data
PV = $20,000
Number of years = 5 years
r = 6.5%
FV = ?
a. compounded semiannually
n = 5 x 2 = 10 compounding periods
r = 6.5% / 2 = 3.25%
FV = $20,000 x ( 1 + 3.25% )^10 = $27,538
b. compounded quarterly
n = 5 x 4 = 20 compounding periods
r = 6.5% / 4 = 1.625%
FV = $20,000 x ( 1 + 1.625% )^20 = $27,608
c. compounded monthly
n = 5 x 12 = 60 compounding periods
r = 6.5% / 12 = 0.542%
FV = $20,000 x ( 1 + 0.542% )^60 = $27,662
d. compounded continuously.
FV = Pe^Yr = $20,000 x 2.71828 = $54,366
2.71828 is a constant value for continuous compounding
