Question

If you have $20,000 to invest for 4 years and can chose either an investment in alternative A that pays interest at a rate of 9% compounding monthly, or investment B that has an interest rate of 9% compounding annually, which investment should you chose?

A	Investment Alternative A.

B	Investment Alternative B.

C	Either one given they both have the same effective annual rate (EAR).

D	Answer cannot be determined given the information provided.

Answer 1

ALTERNATIVE A.
MONTHLY COMPOUNDING
Future Value = C*[(1+(r/m))^mt]
where C is the present value that is 20000
r is the interest rate that is .09
t is the year that is 4
m is the compounding period that is 12
Future value = 20000*[(1+(.09/12))^48]
Future value = 20000*[(1.0075)^48]
Future value = $28628.11.
The future value is $28628.11.

ALTERNATIVE B.
ANNUAL COMPOUNDING
Future Value = C*[(1+(r/m))^mt]
where C is the present value that is 20000
r is the interest rate that is .09
t is the year that is 4
m is the compounding period that is 1
Future value = 20000*[(1.09)^4]
Future value = $28231.63
The future value is $28231.63.

A) INVESTMENT ALTERNATIVE A.