Question

A month from now, you plan to begin saving for your retirement by making a deposit into a new savings account that has an expected return of 5% compounded monthly. You plan to continue depositing the same amount each month until you retire in 35 years. You expect to make withdrawals in the amount of $15,000 from your savings account every year for 40 years after you retire. Assume you were asked to find the amount you will need to deposit into your savings account each month until you retire in order to fund your retirement. In your solution, you would need to use the annuity present value equation to find the present value at your retirement date of the withdrawals you expect to make each year during your retirement. What interest rate would you use in this equation?

Answer 1

Step-1 (Calculation of present value of the Yearly withdrawal on the date of retirement).

Present value of the annuity =

here in the question the interest rate is 5% per annum , compunded monthly. But the withdrawal will be yearly basis.

Hence for calculating the present value of the Yearly withdrawal on the date of retirement, we should take the annual effective interest rate.

yearly nominal rate = 5%

Monthly interest rate = 5%/12 = 0.4167% or 0.004167

Annual Effcetive interest rate = (1+0.004167)^12-1 = 0.0512 or 5.12% per annum.

hence, Present value of the annuity =

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Step-2(calculation of amount tobe deposited in each month)

Let the Amount to be deposited in each month = A

Monthly interest rate = 5%/12 = 0.4167% or 0.004167(r)

Total compounding period (n) = 35 year *12 times a year = 420

Future value of annuity =

=>Monthly savings = $223 (round off)