if you invest $8,000 for 30 months and recieve $1,000 in simple interest , what was the interest rate per year?

Answer 1

Let S = amount of money at the end of the time period

So = the amount of money invested at the beginning

I = Interest Rate

t = time

Then for simple interest for 30 months or 2.5 years S = So(1 + I)t

or

9000 = 8000(1 + I)2.5 or 9000/8000 = (1 + I)2.5 = 1.125

Take the logarithm of both sides to get log(1.125) = 2.5log(1 + I) or .02046 = log(1 + I)

Take each side as the exponent of 10 to get 1.04824 = 1 + I So, I = .04824

To simplify, the yearly interest rate is .04824 or basically 4.824% APR interest rate