Compound Interest Formula
Calculate compound interest using the A = P(1 + r/n)^(nt) formula. Evaluate future value of investments with different compounding frequencies and time periods.
Finance
Detailed Explanation
Compound Interest Formula
The standard compound interest formula is:
A = P * (1 + r/n)^(n*t)
Where:
- P = principal (initial investment)
- r = annual interest rate (as decimal)
- n = compounding frequency per year
- t = time in years
- A = final amount
Example: Savings Account
Invest $10,000 at 5% annual rate, compounded monthly, for 10 years:
10000 * (1 + 0.05/12)^(12*10) = 16470.09
The investment grows to approximately $16,470.
Compounding Frequencies
| Frequency | n | Expression | Result |
|---|---|---|---|
| Annually | 1 | 1000*(1+0.08/1)^(1*5) |
1469.33 |
| Semi-annually | 2 | 1000*(1+0.08/2)^(2*5) |
1480.24 |
| Quarterly | 4 | 1000*(1+0.08/4)^(4*5) |
1485.95 |
| Monthly | 12 | 1000*(1+0.08/12)^(12*5) |
1489.85 |
| Daily | 365 | 1000*(1+0.08/365)^(365*5) |
1491.76 |
Continuous Compounding
For continuous compounding, the formula simplifies to:
A = P * exp(r * t)
Example: $1,000 at 8% for 5 years continuously:
1000 * exp(0.08 * 5) = 1491.82
Finding the Interest Earned
Subtract the principal from the final amount:
10000 * (1 + 0.05/12)^(12*10) - 10000 = 6470.09
Use Case
A financial planner comparing investment options by evaluating compound interest at different rates and compounding frequencies.