Question

Find the future values of the following ordinary annuities:

1. FV of $400 paid each 6 months for 5 years at a nominal rate of 9% compounded semiannually. Do not round intermediate calculations. Round your answer to the nearest cent.

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2. FV of $200 paid each 3 months for 5 years at a nominal rate of 9% compounded quarterly. Do not round intermediate calculations. Round your answer to the nearest cent.

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3. These annuities receive the same amount of cash during the 5-year period and earn interest at the same nominal rate, yet the annuity in part b ends up larger than the one in part a. Why does this occur?

Answer 1

a.Information provided:

Semi-annual payment= $400

Time= 5 years*2= 10 semi-annual periods

Interest rate= 9%/2= 4.50% per semi-annual period

The question is solved by computing the future value of ordinary annuity. Ordinary annuity refers to annuity payments paid at the end of each year.

Enter the below in a financial calculator in END mode to calculate the future value:

PMT= -400

N= 10

I/Y= 4.50

Press the CPT key and FV to calculate the future value.

The value obtained is 4,915.28

Therefore, the future value is $3,814.79.

b.Information provided:

Quarterly payment= $200

Time= 5 years*4= 20 quarters

Interest rate= 9%/4= 2.25% per quarter

The question is solved by computing the future value of ordinary annuity. Ordinary annuity refers to annuity payments paid at the end of each year.

Enter the below in a financial calculator in END mode to calculate the future value:

PMT= -200

N= 20

I/Y= 2.25

Press the CPT key and FV to calculate the future value.

The value obtained is 4,982.30.

Therefore, the future value is $4,982.30.

c.The annuity in part b is larger than one in part a because of the difference in compounding periods. The more the compounding periods, higher the effective rate of interest. Higher the effective rate of interest, higher the interest and future values.