Question

How much should you invest today if, in 6 years, you want to have $4000 in an account that pays 2.9% interest compounded quarterly? Assume that you will not make any payments into the account.

Answer 1

$3363.30.

Explanation:

The equation for the amount after 6 years is:

4000 = P( 1 + 0.029/4)^(6*4). where P is the amount you want to invest now.

P = 4000 / (1 + 0.029/4)^24)

= 3363.30

Answer 2

$3363.30

Explanation:

Let's begin with the compound amount formula:

A = P(1 + r/n)^(nt), where n is the number of times interest is compounded per year, t is the number of years, P is the initial investment amount, and r is the interest rate as a decimal fraction.

Solving for P, we get

A

P = ----------------------

(1 + r/n)^(nt)

and so, with A = $4,000, r = 0.029, n = 4 and t = 6, we get:

$4,000

P = ----------------------------- = ($4,000) / (1.00725^24) , or

(1 + 0.029/4)^(4*6)

P = $4,000 / 1.1893 = $3363.30

If you invest $3363.30 today, 2.9% compounded quarterly for 6 years, you will have $4000 after that period of time.