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.

Answer 1

After Retirement,

Monthly Withdrawal = $10,000

Time Period = 30 years

Calculating Value of Annuity at the start of Retirement,

Present Value = P[1 - (1+r)^-n]/r

Present Value = 10,000[1 - (1 + 0.072/12)^-360]/(0.072/12)

Present Value(start of Retirement) = $3,561,293

From today to retirement,

Time Period = 40 years

Interest Rate = 12.60%

Future Value Required = $3,561,293

So,

Annuity Payment = (0.126/12)(3,561,293)/((1 + 0.126/12)⁴⁸⁰ - 1)

Monthly Deposit Required = $250.18