Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. Essentially, it means earning “interest on interest,” which can cause investments to grow at a faster rate compared to simple interest, which is calculated only on the principal amount.
Compound Interest Formula
The formula to calculate compound interest is:
A=P(1+rn)ntA = P \left(1 + \frac{r}{n}\right)^{nt}A=P(1+nr)nt
Where:
- AAA is the amount of money accumulated after nnn years, including interest.
- PPP is the principal amount (the initial sum of money).
- rrr is the annual interest rate (decimal).
- nnn is the number of times that interest is compounded per year.
- ttt is the time the money is invested or borrowed for, in years.
Example Calculation
If you want to calculate how much $1,000 will grow to in 5 years with an annual interest rate of 5%, compounded monthly, you would use the formula as follows:
- Convert the annual rate from a percentage to a decimal: r=5100=0.05r = \frac{5}{100} = 0.05r=1005=0.05
- Identify the number of times interest is compounded per year: n=12n = 12n=12
- Identify the number of years the money is invested or borrowed: t=5t = 5t=5
Plug these values into the formula:
A=1000(1+0.0512)12×5A = 1000 \left(1 + \frac{0.05}{12}\right)^{12 \times 5}A=1000(1+120.05)12×5
Now, let’s compute this step-by-step:
- Calculate the monthly interest rate: 0.0512=0.004167\frac{0.05}{12} = 0.004167120.05=0.004167
- Calculate the exponent: 12×5=6012 \times 5 = 6012×5=60
- Calculate the base plus the monthly interest rate: 1+0.004167=1.0041671 + 0.004167 = 1.0041671+0.004167=1.004167
- Raise the base to the power of 60: 1.00416760≈1.2831.004167^{60} \approx 1.2831.00416760≈1.283
- Multiply this by the principal: 1000×1.283=12831000 \times 1.283 = 12831000×1.283=1283
So, the amount accumulated after 5 years is approximately $1,283.
Compound interest can significantly increase the amount of money you earn on savings or investments over time, especially when the interest is compounded frequently and the investment period is long.
