Question

You are planning to retire in twenty years. You'll live ten years after retirement. You want

to be able to draw out of your savings at the rate of $10,000 per year. How much would

you have to pay in equal annual deposits until retirement to meet your objectives?

Assume interest remains at 9%.

Answer 1

Part A

Cash flow = $ 10000

Periods = 10

Payout Annuity : you have an investment intially and it gives cash flows over the periods

Present value of Annuity

Particulars	Amount
Cash Flow	$          10,000.00
Int Rate	9.0000%
Periods	10

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
= $ 10000 * [ 1 - [(1+0.09)^-10]] /0.09
= $ 10000 * [ 1 - [(1.09)^-10]] /0.09
= $ 10000 * [ 1 - [0.4224]] /0.09
= $ 10000 * [0.5776]] /0.09
$64,176.54

r - Int rate per period
n - No. of periods

If he have an amount of $ 64176.54 at the time of retirement , he can receive $ 10000 over the next 10 years

Part B

FV of Annuity :
Annuity is series of cash flows that are deposited at regular intervals for specific period of time.

Annuity Amount = $ 64176.54

Period = 20

Particulars	Amount
FV of Annuity	$       64,176.54
Int Rate	9.000%
Periods	20

FV of Annuity = Cash Flow * [ [(1+r)^n ] - 1 ] /r
$64176.54 = Cash Flow * [ [ ( 1 + 0.09 ) ^ 20 ] - 1 ] / 0.09
$64176.54 = Cash Flow * [ [ ( 1.09 ) ^ 20 ] - 1 ] / 0.09
$64176.54 = Cash Flow * [ [ ( 5.6044 ] - 1 ] / 0.09
$64176.54 = Cash Flow * [ 4.6044 ] / 0.09
Cash Flow = $ 64176.54 * 0.09 / 4.6044
Cash Flow = $ 1254.43

r - Int rate per period
n - No. of periods

If he deposite $ 1254.43 over the next 20 years he can have the $ 64176.54 in his account at the time of retirement.

Please comment if any further assistance is required