Math

posted by .

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.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. business math

    Meg's pension plan is an annuity with a guaranteed return of 7% interest per year (compounded monthly). She would like to retire with a pension of $20000 per month for 20 years. If she works 28 years before retiring, how much money …
  2. bus math

    Meg's pension plan is an annuity with a guaranteed return of 7% interest per year (compounded monthly). She would like to retire with a pension of $20000 per month for 20 years. If she works 28 years before retiring, how much money …
  3. math

    Meg's pension plan is an annuity with a guaranteed return of 7% interest per year (compounded monthly). She would like to retire with a pension of $20000 per month for 20 years. If she works 28 years before retiring, how much money …
  4. math

    Meg's pension plan is an annuity with a guaranteed return of 6% per year (compounded quarterly). She would like to retire with a pension of $50,000 per quarter for 15 years. If she works 31 years before retiring, how much money must …
  5. Finance

    Meg's pension plan is an annuity with a guaranteed return of 7% interest per year (compounded monthly). She would like to retire with a pension of $90000 per month for 25 years. If she works 33 years before retiring, how much money …
  6. calculus

    Meg's pension plan is an annuity with a guaranteed return of 4% per year (compounded quarterly). She would like to retire with a pension of $20,000 per quarter for 10 years. If she works 30 years before retiring, how much money must …
  7. Math

    Meg's pension plan is an annuity with a guaranteed return of 7% per year (compounded quarterly). She would like to retire with a pension of $20,000 per quarter for 15 years. If she works 31 years before retiring, how much money must …
  8. finance math

    Meg's pension plan is an annuity with a guaranteed return of 7% interest per year (compounded annually). She would like to retire with a pension of $30000 per annum for 15 years. If she works 31 years before retiring, how much money …
  9. Business Math

    Meg's pension plan is an annuity with a guaranteed return of 3% per year (compounded quarterly). She would like to retire with a pension of $50,000 per quarter for 10 years. If she works 26 years before retiring, how much money must …
  10. Business Calc

    Meg's pension plan is an annuity with a guaranteed return of 3% per year (compounded quarterly). She would like to retire with a pension of $30,000 per quarter for 5 years. If she works 25 years before retiring, how much money must …

More Similar Questions