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Math

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Meg's pension plan is an annuity with a guaranteed return of 9% interest per year (compounded semi-annually). She would like to retire with a pension of $70000 per semi-annum for 25 years. If she works 45 years before retiring, how much money must she and her employer deposit per semi-annum? (

  • Math -

    Assume the 9% per annum interest stays fixed for the 70 years of Meg's life.

    D=semi-annual deposit (in first 45 years)
    =70000
    m=number of periods while working = 2*45=90
    W=semi-annual withdrawal (in last n=25 years)
    n=number of periods while retired = 2*25=50
    A=amount accumulated on Meg's retirement
    R=semi-annual interest rate = 1.045
    Capital required on Meg's retirement,

    First calculate A,
    A=W(R^n-1)/(R-1)=70000*(1.045^50-1)/(1.045-1)
    =$12,495,211.98

    To accumulate A over 45 years:
    12495211.98=D(R^m-1)/(R-1)=D(1.045^90-1)/(1.045-1)
    D=12495211.98(1.045-1)/(1.045^90-1)
    =$10,910.286

    Check me.

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