Question

A year 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 7.5% compounded monthly. You plan to continue depositing the same amount each year until you retire in 30 years. You expect to make withdrawals in the amount of $200 from your savings account every week for 45 years after you retire. Assume you were asked to find the amount you will need to deposit into your savings account each year 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 week during your retirement. What interest rate would you use in this equation? Do not round intermediate calculations. Round the final answer to 2 decimal places. Omit the % sign in your response. For example, an answer of 15.39% should be entered as 15.39

Answer 1

The total investment horizon is 30 years staring from today .

an total withdrawl horizon is 45 years on weekly basis.

At first we convert 7.5 % compounded montly to yearly APR .

EIR = (1+r/m)^m -1

or (1+ 0.075/12)^12 -1

or 7.763 % annualy is the rate we are going to use for calculations .

Now total number of withdrawls we have = 45 years x 52 weeks = 2340 withdrawls

Sum of withdrawl = $200

I/Y weekly rate to be used = 7.763/52 = 0.1493% on weekly basis

So the target investment corpus is

200= Px0.001493/(1- (1+0.001493)^-2340

= $129876.76 is the target investment .

Now we have to find the yearly deposits to meet the target.

FV = 129876.76

N = 30 years

Rate = 7.763 % on yearly basis

So we know

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

PMT = FV / ((1+r)^n-1)/r

or

PMT = 129876.76 / ((1+0.07763)^30 -1 )/0.07763))

PMT = $1197.30 per year