To calculate the compound interest for a loan, we can use the formula:
A = P (1 + r/n) ^ (nt)
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times interest is compounded per year.
- t is the number of years the money is borrowed or invested.
For this example:
- P = 10000
- r = 0.10 (10 percent)
- n = 1 (interest is compounded annually)
- t = 3
Plugging in these values:
A = 10000 (1 + 0.10/1) ^ (1 * 3)
A = 10000 (1 + 0.10) ^ 3
A = 10000 (1.10) ^ 3
A = 10000 * 1.331
A ≈ 13310
Now, to find the compound interest earned, we subtract the principal from the total amount:
Compound Interest = A – P
Compound Interest ≈ 13310 – 10000 = 3310
Therefore, the compound interest on a three-year loan of $10,000 at a 10 percent annual interest rate is approximately $3,310.