What is the compound interest on a three-year, $100.00 loan at a 10 percent annual interest rate?

To calculate compound interest, we use the formula:

[ A = P (1 + r)^n ]

where:

– ( 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 years the money is invested or borrowed.

For your question:

– ( P = 100 )

– ( r = 0.10 ) (10 percent as a decimal)

– ( n = 3 )

Plugging the values into the formula:

[ A = 100 (1 + 0.10)^3 ]

[ A = 100 (1.10)^3 ]

[ A = 100 times 1.331 ]

[ A approx 133.10 ]

Now, to find the compound interest, we subtract the principal from the total amount:

[ text{Compound Interest} = A – P = 133.10 – 100 = 33.10 ]

So, the compound interest on a three-year, $100.00 loan at a 10 percent annual interest rate is $33.10.