To calculate compound interest, you use the formula:
A=P(1+rn)ntA=P\left(1+\frac{r}{n}\right)^{nt}A=P(1+nr)nt
Where:
- AAA = the future value of the investment/loan, including interest
- PPP = the principal amount (initial investment or loan)
- rrr = annual interest rate (decimal)
- nnn = number of times interest is compounded per year
- ttt = number of years the money is invested or borrowed for
The compound interest earned is then:
Compound Interest=A−P=P((1+rn)nt−1)\text{Compound Interest}=A-P=P\left(\left(1+\frac{r}{n}\right)^{nt}-1\right)Compound Interest=A−P=P((1+nr)nt−1)
Example:
If you invest $10,000 at an annual interest rate of 5%, compounded annually for 3 years:
Compound Interest=10,000×((1+0.05)3−1)=10,000×(1.157625−1)=1,576.25\text{Compound Interest}=10,000\times \left((1+0.05)^3-1\right)=10,000\times (1.157625-1)=1,576.25Compound Interest=10,000×((1+0.05)3−1)=10,000×(1.157625−1)=1,576.25
So, the interest earned after 3 years is $1,576.25
Steps to Calculate Compound Interest:
- Identify the principal amount PPP.
- Convert the interest rate to decimal form rrr.
- Determine the number of compounding periods per year nnn.
- Determine the total number of years ttt.
- Plug these values into the formula and solve for AAA.
- Subtract the principal PPP from AAA to get the compound interest.
Additional Notes:
- Interest can be compounded annually, semiannually, quarterly, monthly, daily, etc., depending on nnn.
- The Rule of 72 can estimate how long it takes for an investment to double by dividing 72 by the interest rate percentage.
- Tools like Excel or online calculators can automate these calculations
