Final answer:
The future value of Heather's $5,000 investment at a compound interest rate of 9.8%, compounded annually for 3 years, is approximately $7,037.22.
Step-by-step explanation:
If Heather invests $5,000 in a savings account at a 9.8% compound interest rate, compounded annually, for 3 years, we can calculate the future value of her investment using the compound interest formula:
FV = P (1 + r/n)nt
Where:
- FV is the future value of the investment,
- P is the principal amount ($5,000),
- r is the annual interest rate (9.8%),
- n is the number of times that interest is compounded per year (1 for annually), and
- t is the number of years the money is invested (3).
Let's plug in the values:
FV = $5,000 (1 + 0.098/1)1*3 = $5,000 (1 + 0.098)3 = $5,000 * 1.0983
After calculating, you'll find that:
FV ≈ $7,037.22
Therefore, after three years, Heather's investment will grow to approximately $7,037.22.