Final answer:
You would calculate the balance after three years by applying the compound interest formula to the initial deposit of $2,000 with an annual rate of 6.5% compounded semi-annually, resulting in a total amount of $2,436.80.
Step-by-step explanation:
If you deposit $2,000 in an account that pays 6.5% annual interest compounded semi-annually, the balance after three years can be calculated using 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.
Plugging the values into the formula, we get:
A = $2,000(1 + \frac{0.065}{2})^{2\times3}
A = $2,000(1 + 0.0325)^{6}
A = $2,000(1.0325)^{6}
A = $2,000\times1.218402
A = $2,436.80
The balance in the account after three years will be $2,436.80.