Question

You plan to make a deposit todeer so that w You can withdraw evere year for zoyears you with drawal at the end of year 1 will be 3000 and will increase by $100 every year, How much do you need to deposit today if the interest rate is 8% compounded annually?

Answer 1

Withdrawal at the end of year – 1 = $3,000

It will increase by $100 every year

Number of years = 20 years

Rate of interest = 8%

How much do you need to deposit today?

Calculate the Present Worth.

This is a case of arithmetic gradient cash flows.

PW = $3,000 (P/A, 8%, 20) + $100 (P/G, 8%, 20)

PW = $3,000 (9.8181) + $100 (69.0898)

PW = $36,363.28 or rounded off to $36,363

You need to deposit today $$36,363.

Alternatively it can be calculated as under

Convert the gradient cash flows into uniform cash flows.

A = A1 + G (A/G, 8%, 20)

A = 3,000 + 100 (7.0369) = 3,703.69

Now calculate the PW.

PW = A (P/A, 8%, 20)

PW = 3,703.69 (9.8181)

PW = 36,363.19 or rounded off to $36,363