Question

Using a 5% annual compound interest rate, what investment today is needed in order to withdraw $3,000 annually
a. for 10 years? $enter a dollar amount
b. for 10 years if the first withdrawal does not occur for 3 years? $enter a dollar amount

Round your answers to the nearest dollar. The tolerance is ± 2.

Answer 1

- Perioidic Withdrawal Annually= $3000

a). Calculating the Present Value of withdrawal for 10 years :-

Where, C= Periodic Payments = $3000

r = Periodic Interest rate = 5%

n= no of periods = 10 years

Present Value = $23,165.20

So, the amount needed to investment today is $23,165.20

b). Withdrawal annually for 10 years if the first withdrawal does not occur for 3 years.

Present Value of annuity withdrawal is calculated at year end 2 as the first withdrawal occur at the end of 3 year. So, From year 2 to year 0 we will discount the Present Value of annuity.

Calculating the Present Value of withdrawal:-

Where, C= Periodic Payments = $3000

r = Periodic Interest rate = 5%

n= no of periods = 10 years

m = no of periods of discounting = 2

Present Value = $21011.52

So, the amount needed to investment today is $21,011.52

If you need any clarification, you can ask in comments.    

If you like my answer, then please up-vote as it will be motivating