Question

(b) You plan to save 10% of your yearly salary of $80,000 for retirement in a mutual fund earning 9% per year. Your salary will increase by 5% per year for 30 years when you retire. How much money will you have when you retire? (b) How much can you spend per year if you will live for 25 years after retirement if you can earn 8% on your money?

Answer 1

Annual Salary in Year 1= $80,000

Annual Saving in Year 1 = 0.10(80000) = $8,000

Salary Growth Rate = Saving Growth Rate = 5%

Interest Rate on Mutual Fund = 9% annually

Time Period = 30 years

a.

Calculating Future Value,

Future Value of Growing Annuity = P[((1 + r)ⁿ - (1 + g)ⁿ)/(r - g)]

Future Value = 8000[((1.09)³⁰ - (1.05)³⁰)/(0.09 - 0.05)]

Future Value = $1,789,147.22

b.

Time Period after retirement = 25 years

Interest Rate = 8% annually

Present Value of Annuity = $1,789,147.22

Calculating Annuity Payment,

Annuity Payment = r(PV)/1 - (1 + r)^-n

Annuity Payment = 0.08(1,789,147.22)/1 - (1.08)^-25

Annuity Payment = $167,605.13

So,

Annually one can spend $167,605.13