The company you work for will deposit $500 at the end of eachmonth into your...

The company you work for will deposit $500 at the end of each month into your retirement fund. Interest is compounded monthly. You plan to retire 12 years from now and estimate that you will need $3,000 per month out of the account for the next 10 years following your retirement. If the account pays 7.25% compounded monthly, how much (in addition to your company deposit)do you need to put into the account on monthly basis in order to meet your objective?

Expert Solution

PV of Annuity:

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here cash flows are happened at the end of the period. PV of annuity is current value of cash flows to be received at regular intervals discounted at specified int rate or discount rate to current date.

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
r - Int rate per period
n - No. of periods

Particulars	Amount
Cash Flow	$ 3,000.00
Int Rate	0.6042%
Periods	120

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
= $ 3000 * [ 1 - [(1+0.006)^-120]] /0.006
= $ 3000 * [ 1 - [(1.006)^-120]] /0.006
= $ 3000 * [ 1 - [0.4854]] /0.006
= $ 3000 * [0.5146]] /0.006
= $ 255534.36
Monthly deposit required:

FV of Annuity :

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here deposits are made at the end of the period. FV of annuity is future value of cash flows deposited at regular intervals grown at specified int rate or Growth rate to future date.

FV of Annuity = CF [ (1+r)^n - 1 ] / r
r - Int rate per period
n - No. of periods

Particulars	Amount
FV of Annuity	$ 255,534.36
Int Rate	0.6042%
Periods	144

FV of Annuity = Cash Flow * [ [(1+r)^n ] - 1 ] /r
$255534.36 = Cash Flow * [ [ ( 1 + 0.006 ) ^ 144 ] - 1 ] / 0.006
$255534.36 = Cash Flow * [ [ ( 1.006 ) ^ 144 ] - 1 ] / 0.006
$255534.36 = Cash Flow * [ [ ( 2.3807 ] - 1 ] / 0.006
$255534.36 = Cash Flow * [ 1.3807 ] / 0.006
Cash Flow = $ 255534.36 * 0.006 / 1.3807
Cash Flow = $ 1118.19

Additional deposit = $ 1118.19 - $ 500

= $ 618.19

Additional deposit ( In addition to $ 500) to be made is $ 618.19

jeff jeffy answered 2 years ago

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