Question

In: Finance

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?

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

x

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)

i

6%/12

=

0.005

=

155.982898

n

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

i

6%/12

=

0.005

=

1991.490734

n

40*12

=

480

Thus,

Investment at the end of each month

$ 391.62

jeff jeffy answered 2 years ago

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