Final answer:
To calculate the future value of $8,906.54 invested for 9 years at an annual interest rate of 3% compounded semi-annually, you use the compound interest formula and find that the amount in the account after 9 years would be $11,663.78.
Step-by-step explanation:
The student has asked to find the future value of an investment of $8,906.54 after 9 years with an interest rate of 3% compounded semi-annually. To solve this, we use the formula for compound interest which is:
A = P(1 + 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.
For this example:
- P = $8,906.54
- r = 0.03 (3% as a decimal)
- n = 2 (since the interest is compounded semi-annually)
- t = 9
So the equation becomes:
A = 8906.54(1 + 0.03/2)^2*9
Now, calculate the new value of A:
A = 8906.54(1 + 0.015)^18
A = 8906.54(1.015)^18
A = 8906.54 * (1.308287)
A = $11,663.78
The future value of the investment after 9 years is $11,663.78.