Question

A week from now, you plan to begin saving for your retirement by depositing $200 into a new savings account that has an expected return of 7.75% compounded monthly. You plan to continue depositing the same amount each week until you retire in 40 years. You expect to make withdrawals from your savings account every year for 35 years after you retire. Assume you were asked to find the amount you will be able to withdraw each year from your savings account during your retirement. In your solution, you would need to find the future value of your savings account at your retirement date by using the annuity future value equation. What interest rate would you use in this equation?

Answer 1

Assuming the ask is to find the applicable interest rate only

The given Interest Rate is 7.75% pa with monthly compounding

Effective Annual Rate =(1+7.75%/12)^12-1=8.0313% pa

So we have the effective Interst Rate of 8.0313% pa

Now the Annuity is weekly, so wee need to find an weekly

interest rate that will give effective Annual rate of 8.0313%

with weekly compounding.

Assume the weekly rate is x, with weekly compounding

So we have the effective Interst=(1+x)^52-1=8.0313%

or (1+x)^52=1+8.0313%

or, (1+x)^52=1.080313

or , (1+x)=1.080316^(1/52)=1.0014864

or , x=0.14867% per week.

So the interest rate to be used to find the FV of the weekly

Annuity will be =0.14867% per week, compounded weekly.