Future Value of Multiple Annuities Assume that you contribute $200 per month to a retirement plan for 15 years.Then you are able to increase the contribution to $400 per month for another 25 years.Given a 5 percent interest rate,what is the value of your retirement plan after 40 years?
A)$424,305.97
B)$24,159.95
C)$28,475.66
D)$72,479.86

Question

Quizplus · Accepted Answer

To calculate the future value of multiple annuities, we use the formula:

FV = Pmt x (((1 + r)^n - 1) / r)

where,

Pmt = Payment per period
r = Interest rate per period
n = Total number of periods

In this case,

For the first 15 years, 
Pmt = $200
r = 5%/12 = 0.41667% (monthly interest rate)
n = 15 x 12 = 180 (total number of monthly payments)

FV1 = 200 x (((1 + 0.41667%)^180 - 1) / 0.41667%) = $66,393.77

For the next 25 years,
Pmt = $400
r = 5%/12 = 0.41667% (monthly interest rate)
n = 25 x 12 = 300 (total number of monthly payments)

FV2 = 400 x (((1 + 0.41667%)^300 - 1) / 0.41667%) = $357,912.20

Therefore, the total future value of the retirement plan after 40 years is:

FV = FV1 + FV2 = $424,305.97

So, the best choice is (A).

Future Value of Multiple Annuities Assume That You Contribute $200