Given:
Principal = $54,000
Time = 9 years
Rate of compound interest = 12% per annum.
To find:
The compound interest.
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 principal, r is the rate of interest in decimal, n is the number of time interest compounded and t is the number of years.
The interest is compounded annually, so
.
Substituting
in the above formula, we get
![A=54000\left(1+\dfrac{0.12}{1}\right)^{1(9)}](https://tex.z-dn.net/?f=A%3D54000%5Cleft%281%2B%5Cdfrac%7B0.12%7D%7B1%7D%5Cright%29%5E%7B1%289%29%7D)
![A=54000\left(1.12\right)^{9}](https://tex.z-dn.net/?f=A%3D54000%5Cleft%281.12%5Cright%29%5E%7B9%7D)
![A=149746.252902](https://tex.z-dn.net/?f=A%3D149746.252902)
![A\approx 149746.25](https://tex.z-dn.net/?f=A%5Capprox%20149746.25)
The amount after 9 years is $149746.25.
Now, the compound interest is:
![C.I.=A-P](https://tex.z-dn.net/?f=C.I.%3DA-P)
Where, C.I. is compound interest, A is amount and P is principal.
![C.I.=149746.25-54000](https://tex.z-dn.net/?f=C.I.%3D149746.25-54000)
![C.I.=95746.25](https://tex.z-dn.net/?f=C.I.%3D95746.25)
Therefore, the compound interest is $95746.25.