How long will it take 500 dollars to double if it is invested at 7% interest compounded semi-annually

11 half years

Step-by-step explanation:

The formula for compound interest is

A = P(1+r/n)^(nt), with r representing the interest rate, n being the number of times interest is applied over the time period, and t being the amount of time periods.

If we make the time period a half year (so interest is compounded once per time period), n=2. Then, our interest rate is 7%, or 0.07 (to convert from percent to decimal, simply divide by 100). Our starting amount is 500, and we want it to double, making it 1000. Our formula is thus

1000 = 500 (1+0.07)^(t)

divide both sides by 500

2 = (1+0.07)^(t)

2 = (1.07)^(t)

Using logarithms, we can say that

and using a calculator, we get

10.24 = t

Since interest is only compounded once per time period, though, we have to round up to make sure it doubles, so t = 11