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March 28, 2017

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Suppose a young couple deposits $700 at the end of each quarter in an account that earns 7.1%, compounded quarterly, for a period of 6 years. After the 6 years, they start a family and find they can contribute only $200 per quarter. If they leave the money from the first 6 years in the account and continue to contribute $200 at the end of each quarter for the next 18½ years, how much will they have in the account (to help with their child's college expenses)?

  • math - ,

    Part 1:
    R=$700 per quarter
    i=7.1%/4 per quarter
    n=6*4=24 quarters
    S=future value
    =R((1+i)^n-1)/i
    =700((1+.071/4)^24-1)/(.071/4)
    =$20,720.40

    After 6 years,
    S1=future value (after 18.5 years) of initial investment
    =S(1+i)^n
    =$20720.40(1+.071/4)^74
    =$76179.91

    R=$200 per quarter
    i=7.1%/4 per quarter
    n=18.5*4=74 quarters
    S2=future value for further contributions
    =200((1+.071/4)^74-1)/(.071/4)
    =$30,158.48

    Total future value
    = $76179.91+$30158.48
    = $106,338.39

    Check the calculations please.

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