I invested $45,6000 at 18% to be compounded semi-annually. What will be the value of my investment in four years?
what is 456000(1.09)^8 ?
To calculate the future value of your investment, you can use the compound interest formula:
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
where:
- A is the future value of the investment,
- P is the principal amount (initial investment),
- r is the annual interest rate (in decimal form),
- n is the number of times the interest is compounded per year, and
- t is the number of years.
In this case, you have:
- P = $45,600,
- r = 0.18 (18% expressed as a decimal),
- n = 2 (semi-annual compounding),
- t = 4 years.
Plugging these values into the formula, we can calculate the future value:
\[
A = 45,600 \left(1 + \frac{0.18}{2}\right)^{(2 \times 4)}
\]
\[
A = 45,600 \left(1 + 0.09\right)^{8}
\]
Now, let's solve the exponent first:
\[
A = 45,600 \times 1.09^{8}
\]
Using a calculator, we find that \(1.09^8 \approx 1.999\).
\[
A = 45,600 \times 1.999
\]
Simplifying the calculation:
\[
A \approx \$91,188
\]
Therefore, the value of your investment after four years will be approximately $91,188.