Question

Find the final amount in the following retirement account, in which the rate of return on the account and the regular contribution change over time.
$470 per month invested at 5%, compounded monthly, for 7 years; then $709 per month invested at 7%, compounded monthly, for 7 years.
What is the amount in the account after 14 years? Please show work.

Answer 1

first 7 years:
i = .05/12 = .004166...
n = 7(12) = 84

amount after 7 years = 470(1.041666...^84 - 1)/.004166..
= 47154.47
This will accumulate for another 7 years at 7% pa, compounded monthly
i = .07/12 = .0058333...
n = 84
amount of first investment
= 47154.47(1.0058333..)^84 = 76861.50

amount of 2nd investment
= 709(1.0058333..^84 - 1)/.005833...
= 76571.28

total = $153,432.77