Final answer:
To determine the future value and interest earned of $8906.54 invested at a 3% interest rate compounded annually for 9 years, we apply the compound interest formula, subtract the initial investment from the result to find the interest earned.
Step-by-step explanation:
To find the future value and interest earned when $8906.54 is invested for 9 years at a 3% interest rate compounded annually, we use the formula for compound interest:
FV = P(1 + r/n)nt
where:
- FV is the future value of the investment,
- P is the principal amount ($8906.54),
- r is the annual interest rate (3% or 0.03),
- n is the number of times that interest is compounded per year (1 for annually),
- t is the time the money is invested for in years (9 years).
Plugging in the values, we get:
FV = $8906.54(1 + 0.03/1)(1)(9)
Calculating the above gives us the future value. Then, to find the interest earned, subtract the original principal from the future value:
Interest Earned = FV - P
This will give us the amount of money that has been earned from interest over the investment period.