# SAT maths problem

• Oct 20th 2010, 09:56 AM
geton
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?
• Oct 20th 2010, 12:02 PM
emakarov
I believe you are right.
• Oct 20th 2010, 06:39 PM
Wilmer
Quote:

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