# Math Help - SAT maths problem

1. ## Interest rate problem

How much interest will $1000 earn in one year at an annual rate of 8%; if interest is compounded every 6 months? I've thought so far: At 8% in one year interest will be 80. But it is compounded every 6 months. So, after 6 months total amount will be$1040. Again at 8% in next 6 months, the amount will be $1081.6. Therefore, the interest will be$81.6. Is it right?

2. I believe you are right.

3. Originally Posted by geton
At 8% in one year interest will be 80. But it is compounded every 6 months.
So, after 6 months total amount will be $1040. Again at 8% in next 6 months, the amount will be$1081.6
Therefore, the interest will be \$81.6. Is it right?
Correct. Formula for Future Value of amount A:
FV = A(1 + i)^n ; in your case, A=1000, i = .08/2 = .04, n = 2 (2 semiannual periods); so:
FV = 1000(1.04)^2 = 1081.60

If 6 years, then n=12 and:
FV = 1000(1.04)^12 = 1601.03