Example 9

Using the Compound Interest Formula to Solve for the Principal

A 529 Plan is a college-savings plan that allows relatives to invest money to pay for a child's future college tuition; the

account grows tax-free. Lily wants to set up a 529 account for her new granddaughter and wants the account to grow

to $40,000 over 18 years. She believes the account will earn 6% compounded semi-annually (twice a year). To the

nearest dollar, how much will Lily need to invest in the account now?

Solution The nominal interest rate is 6%, so r = 0.06. Interest is compounded twice a year, so n = 2.

We want to find the initial investment, P, needed so that the value of the account will be worth $40,000 in 18 years.

Substitute the given values into the compound interest formula, and solve for P.

A(t) = P 1 + _r

n nt Use the compound interest formula.

40,000 = P 1 + 0_.0_6_

2

2(18)

Substitute using given values A, r, n, and t.

40,000 = P(1.03)36 Simplify.

_4_0_,0_0_0_

(1.03)36 = P Isolate P.

P $13, 801 Divide and round to the nearest dollar.

Lily will need to invest $13,801 to have $40,000 in 18 years.

Refer to Example 9. To the nearest dollar, how much would Lily need to invest if the account is compounded quarterly?