After 6 years, an investment is worth $8479. If the money was invested at 9% interest compounded semi-annually, what was the initial investment?
Assuming that 9% is the annual interest rate, i.e. r = 0.09,
and that 6 months is one term over which interest is applied,
n = 2 (the number of terms in a year)
y = 6 (the number of years of investment) (and 2*6 = 12 terms of 6 months each)
P = initial investment
A = final return on investment
A = P[1 + (r/n)]^(yn)
8479 = P[1 + (0.09/2)]*(2*6)
8479 = P[1.045]^(12)
8479 = P[1.69588]
P = 8479 / 1.69588
P = 4999.76
Answer: Initial investment was $5,000