Question

# Marie just turned 28 and are now seriously planning for her retirement. Marie wishes to retire...

Marie just turned 28 and are now seriously planning for her retirement. Marie wishes to retire two years earlier than the mandatory retirement age of 65. She hopes to be able to make end-of-month withdrawals from her retirement account of \$25,000 per month for a 30-year period after that.

Marie's plan is to fund her retirement by making monthly deposits between now and when she retires. The initial monthly deposit will be made at the end of the coming month.

How much monthly deposit Marie should make if she can earn 12 % per annum in her retirement account? (Ignore taxes.)

 Let us find the PV of the retirement annuity first. Formula for present value of an anuuity = PV= A [ {(1+k)n-1}/k(1+k)n] PV = Present value of annuity=? A = periodical (monthly) instalments=25,000 k=interest rate=1% per month n=periods=30 years =360 months PV =25000*[(1.01^360-1)/1%*1.01^360 PV=\$2,430,458.28 So Maries needs a fund of \$2,430,458.28 after 35 years. Assume required monthly deposit =A FV= A [ {(1+k)n-1}/k] FV = Future annuity value=2,430,458.28 A = monthly investment =? K=interest rate=1% per month N=periods=35 years=420 months 2,430,458.28=A*[1.01^420-1]/1% A=\$377.93 So Marie needs to make monthly deposit of \$377.93 to get the required retirement fund accumulation.