Answer: 12491.71
Steps:
1) The formula for compound interest is x=P(1+r/n)^nt. This means that the final amount (x) is equal to the initial deposit (P) times the result of 1 plus the interest rate (r) divided by the number of times the interest occurs in a given time period (n) to the power of n times the number of time periods (t).
2)Next we have to plug in our information from the problem. We know that the initial deposit (P) was 6000 and the interest rate (r) is .13 (13%), so we can start by plugging those two in. This will get us x=6000(1+.13/n)^nt. Since it occurs annually, we know that the number of times it occurs each year is n, and we also know that the number of years for which she will leave it (t). This gives us n = 1 (since it happens once per year) and t = 6 (since she is leaving it for 6 years). Plugging this in, we get x = 6000(1+.13/1)^1x6. We can simplify this to x = 6000(1+.13/1)^6 since 1x6 is 6.
3) Finally, we need to solve. If you can use a calculator, you may skip this part. However, if you can’t, it goes like this: First, we need to solve everything within the parentheses. .13/1 is still .13, and once we add in the 1 we get 1.13. This gives us x = 6000(1.13)^6. Next, we need to do the exponent. 1.13^6 is about 2.081952. We are unable to round this number yet in order to keep it accurate. After that, we get x = 6000x2.081952. Multiplying those together, we get 12491.712, which rounds to 12491.71.
Hope this helped