Question

Question: Sandra deposited $605 each month into her retirement, starting her senior year at NYU.  She diversified her portfolio, so the interest rate averaged to a fixed rate of 9.75%.  If she was 20 when she started and continued through to age 68, determine how much interest accumulated to her account

Question:Patel saved $89 per month into her TIAA retirement account for 30 years at a fixed interest rate of 4.89%.  Once she retired, she told TIAA to distribute payments from her account to her in equal amounts over the next 25 years, assuming a fixed interest rate of 4.02%.  How much would TIAA send Patel monthly in order to satisfy her request?

Answer 1

Sandra:-

Annuity per month=A=605

Interest=r=9.75% per annum=0.8125% per month

Starting at age of 20 and ending on age of 68=48 years=576 months

=>n=576 months

Future Value of Annuity

= A*[(1+r)^n-1] / r

=605*[(1+0.008125)^576-1] / 0.008125

=74461.54[(1.008125)^576-1]

=74461.54[105.7513-1]

=7799941

Total principal invested=605*576=348480

Interest accumulated in her account = 7799941-348480 = 7451461

Patel:-

Annuity per month=A=89

Interest=r=4.89% per annum=0.4075% per month

n=30 years=360 months

Future Value of Annuity

=A*[(1+r)^n-1] / r

=89*[(1+0.004075)^360-1] / 0.004075

=21840.49[(1.004075)^360-1]

=21840.49[4.3233-1]

=$72582.51

Now Interest rate=i=4.02% per annum=0.335% per month

Time period=t=25*12=300 months

=>Total initial amount / PVIFA(i,t) = Future equivalent amounts per time perod t

New monthly Receipts:-

=72582.51 / Present Value interest factor of Annuity (0.335%,300 months)

=72582.51 / 189.0567

=$383.92

TIAA would send Patel $383.92 per month to satisfy her request