Given:
![P=\$120,000](https://tex.z-dn.net/?f=P%3D%5C%24120%2C000)
![r=5.3\%](https://tex.z-dn.net/?f=r%3D5.3%5C%25)
![t=8\text{ years}](https://tex.z-dn.net/?f=t%3D8%5Ctext%7B%20years%7D)
To find:
The value of the investment when the interest is compounded annually.
Solution:
The formula for amount is:
![A=P\left(1+\dfrac{r}{n}\right)^{nt}](https://tex.z-dn.net/?f=A%3DP%5Cleft%281%2B%5Cdfrac%7Br%7D%7Bn%7D%5Cright%29%5E%7Bnt%7D)
Where, P is the principal, r is the rate of interest in decimal, n is the number of time interest compounded in an years, and t is the number of years.
The interest is compounded annually. So,
.
Substituting
in the above formula, we get
![A=120000\left(1+\dfrac{0.053}{1}\right)^{1(8)}](https://tex.z-dn.net/?f=A%3D120000%5Cleft%281%2B%5Cdfrac%7B0.053%7D%7B1%7D%5Cright%29%5E%7B1%288%29%7D)
![A=120000\left(1.053\right)^{8}](https://tex.z-dn.net/?f=A%3D120000%5Cleft%281.053%5Cright%29%5E%7B8%7D)
![A=181387.85936](https://tex.z-dn.net/?f=A%3D181387.85936)
![A\approx 181387.86](https://tex.z-dn.net/?f=A%5Capprox%20181387.86)
Therefore, the value of the investment after 8 years is $181,387.86.