Question

I need help on this question please. Thank you!

Catherine Dohanyos plans to retire in 15 years. She will make 15 years of monthly contributions to her retirement account. One month after her last​ contribution, she will begin the first of 10 years of withdrawals. She wants to withdraw ​$3500 per month. How large must her monthly contributions be in order to accomplish her goal if the account earns interest of 7.3% compounded monthly for the duration of her contributions and the 120 months of​ withdrawals?

The amount of her monthly contributions must be?

Answer 1

First we estimate the FW of accumulation at retirement.

Period of deposits=n=15*12=180 months

Rate of interest=i=7.3%/12=0.6083 %=0.006083 per month

Let the deposit per month be R

FW of accumulation=R*(F/A,0.006083,180)

(1 + i) (F/A, i, n)

(F/A, 0.006083, 180) - 1+0.006083)80 1 0,006083 325.350286

FW of accumulation=R*325.350286=325.350286R

Now we calculate the present worth of drawings at retirement

Period of deposits=n=10*12=120 months

Drawing per month=D=$3500

PW of drawings at retirement=D*(P/A,0.006083,120)

1 1+i (P/A, i, n)

(1+0.006083)120 0.006083 (P/A, 0.006083, 120) 84.991765

PW of drawings at retirement=3500*84.991765=$297471.18

Set FW of deposits at retirement=PW of drawings at retirement

325.350286R=297471.18

R=297471.18/325.350286=$914.31

Monthly deposit should be $914.31