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Answer:
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
[tex]log_{1.07} 2 = t[/tex]
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