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A Nationalized Bank offered a pension plan as an ordinary annuity that earned 6.5% compounded annually. A person plans to make equal annual deposits of ` 2000 into this account for 25 years and then make20 equal annual withdrawals, reducing the balance in the account to zero. How much can be withdrawn annually for the next 20 years?
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A Nationalized Bank offered a pension plan as an ordinary annuity that...
Calculation of Pension Plan Withdrawals


Given:


  • The pension plan is an ordinary annuity that earns 6.5% compounded annually

  • Equal annual deposits of ` 2000 will be made for 25 years

  • 20 equal annual withdrawals will be made to reduce the balance in the account to zero



Calculation of Future Value of Annuity:

The future value of the annuity can be calculated using the formula:

FV = Pmt x (((1 + r)^n - 1) / r)



  • Pmt = 2000 (annual deposit)

  • r = 6.5% (annual interest rate)

  • n = 25 (number of years)



Substituting the values in the formula:

FV = 2000 x (((1 + 0.065)^25 - 1) / 0.065) = ` 99497.44


Calculation of Withdrawals:

The withdrawals can be calculated using the formula for the present value of an annuity:

PV = Pmt x ((1 - (1 + r)^-n) / r)



  • Pmt = To be calculated

  • r = 6.5% (annual interest rate)

  • n = 20 (number of years)



Substituting the values in the formula and equating it to the future value of the annuity:

99497.44 = Pmt x ((1 - (1 + 0.065)^-20) / 0.065)

Pmt = 6943.43


Conclusion:

The person can withdraw ` 6943.43 annually for the next 20 years to reduce the balance in the account to zero.
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A Nationalized Bank offered a pension plan as an ordinary annuity that earned 6.5% compounded annually. A person plans to make equal annual deposits of ` 2000 into this account for 25 years and then make20 equal annual withdrawals, reducing the balance in the account to zero. How much can be withdrawn annually for the next 20 years?
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