Question

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You plan to retire in 40 years. After that, you want to receive an annuity of...

You plan to retire in 40 years. After that, you want to receive an annuity of 5000 per month for 25 years, beginning immediately upon retirement. If you can earn 6% per year, compounded monthly, how much must you invest at the end of each month before retirement?

Solutions

Expert Solution

Step-1:Calculation of present value of monthly withdrawl after retirement

Present Value

Monthly withdrawl x Present value of annuity due of 1

$ 5,000

155.982898

$ 7,79,914.49

Working:

Present value of annuity due of 1

((1-(1+i)^-n)/i)*(1+i)

Where,

((1-(1+0.005)^-300)/0.005)*(1+0.005)

6%/12

0.005

155.982898

25*12

300

Step-2:Calculation of monthly saving to reach retirement amount

Monthly saving

Retirement target amount/Future value of ordinary annuity of 1

$ 7,79,914.49

1991.4907

$ 391.62

Working:

Future Value of ordinary annuity of 1

(((1+i)^n)-1)/i

Where,

(((1+0.005)^480)-1)/0.005

6%/12

0.005

1991.490734

40*12

480

Thus,

Investment at the end of each month

$ 391.62

jeff jeffy answered 1 year ago

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