Final answer:
To find the future balance of Amy's investment with compound interest, we use the compound interest formula, where the principal is $1500, the annual interest rate is 6.5%, interest is compounded monthly, and time is 20 years.
Step-by-step explanation:
To calculate the future balance of an investment, with compound interest, we can use the compound interest formula: A = P(1 + \frac{r}{n})^{nt}, where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
In Amy's case, she invested $1500 at an interest rate of 6.5% compounded monthly. This means that P = 1500, r = 0.065 (because 6.5% = 0.065), n = 12 (since interest is compounded monthly), and t = 20.
Substituting these values into the compound interest formula:
A = 1500(1 + 0.065/12)^(12*20)
Calculating this gives us the future balance of the account after 20 years.