Question

A woman plans to retire in 40 years, and she expects to live for 30 years after that. She wants to spend 10,000 a month after she retires. To finance her retirement she is going to invest monthly (with her investment one month from know) over 40 years at 12.6%. After she retires she will move her investment to a more liquid account earning 7.2% a year. Ignore taxes and transaction costs. How much does she have to sabe a month until her retirement.

Finance 311, intermediate finance

Answer 1

Retirement Tenure = 30 years or (30 x 12) = 360 months, Rate of Return post Retirement = 7.2 %

Applicable Monthly Rate = 7.2 / 12 = 0.6 % and Monthly Withdrawals Post Retirement = $ 10000

Total Present Value of Retirement Withdrawals at the end of Year 40 = PV40 = 10000 x (1/0.006) x [1-{1/(1.006)^(360)}] = $ 1473213.568

Let the required monthly savings be $ K. Savings Tenure = 40 years or (40 x 12) = 480 months, Rate of Return during Savings Tenure = 12.6 %

Applicable Monthly Rate = 12.6/12 =1.05 %

Total Future Value of Monthly Savings at the end of year 40 = FV40 = K x (1.0105)^(479) + K x (1.0105)^(478) +..........+ K x (1.0105) + K = K x [{(1.0105)^(480)-1} / {1.0105 - 1}]

Now, PV40 = FV40 so as to conform with the principles of time value of money

Therefore, K x [{(1.0105)^(480)-1} / {1.0105 - 1}] = 1473213.568

K x 14234.66553 = 1473213.568

K = 1473213.568 / 14234.66553 = $ 103.49478 ~ $ 103.495