Susan Wilson wants to accumulate $14,500 by the end of 12 years. If the annual interest rate is 5.70 percent and interest compounds semiannually, how much will she have to invest today to achieve her goal?

She have to invest $7,387 today to achieve goal

Explanation:

Future value is the accumulated value of principal and compounding interest after some period of investment.

Target Future value = A = $14,500

Number of year = 12 years

Yearling compounding = 2 time a year

Total compounding = n = 12 x 2 = 24 compounding periods

Interest rate = r = 5.7% yearly = 5.7% / 2 = 2.85% semiannually

A = P (1 + r) ^n

$14,500 = P (1 + 2.85%) ^24

$14,500 = P x 1.963

P = $14,500 / 1.963

P = 7,386.65

P = 7,387