Question

Future Value of an Annuity for Various Compounding Periods

Find the future values of the following ordinary annuities.

1. FV of $600 each 6 months for 4 years at a nominal rate of 12%, compounded semiannually. Do not round intermediate calculations. Round your answer to the nearest cent.

   $  

2. FV of $300 each 3 months for 4 years at a nominal rate of 12%, compounded quarterly. Do not round intermediate calculations. Round your answer to the nearest cent.

   $  

3. The annuities described in parts a and b have the same amount of money paid into them during the 4-year period, and both earn interest at the same nominal rate, yet the annuity in part b earns more than the one in part a over the 4 years. Why does this occur?

Answer 1

a

FV of annuity	=	P * [ (1+r)^n -1 ]/ r
Periodic payment	P=	$                   600.00
rate of interest per period	r=
Rate of interest per year		12.0000%
Payment frequency		Once in 6 months
Number of payments in a year		2.00
rate of interest per period		0.12*6/12	6.0000%
Number of periods
Number of years		4
Number of payments in a year		2
Total number of periods	n=	8
FV of annuity	=	600* [ (1+0.06)^8 -1]/0.06
FV of annuity	=	5,938.48

Future value is $5,938.48

b

FV of annuity	=	P * [ (1+r)^n -1 ]/ r
Periodic payment	P=	$                   300.00
rate of interest per period	r=
Rate of interest per year		12.0000%
Payment frequency		Once in 3 months
Number of payments in a year		4.00
rate of interest per period		0.12*3/12	3.0000%
Number of periods
Number of years		4
Number of payments in a year		4
Total number of periods	n=	16
FV of annuity	=	300* [ (1+0.03)^16 -1]/0.03
FV of annuity	=	6,047.06

Future value is $6,047.06

c

Difference is due to difference in compounding of interest. More number of compounding intervals in quarterly payment resulted in highe interest.

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