finance

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.

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  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

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