Final answer:
The interest paid in the first year on a $10,500 loan at 11 percent annually compounded interest is $1,155. This is calculated using the simplified compound interest formula for one year with the principal amount multiplied by the annual interest rate.
Step-by-step explanation:
To calculate the interest paid in the first year on a loan with compounded interest, you use the formula for the compound interest A = P(1 + r/n)^(nt) where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. In this case, since the interest is compounded annually, n is 1, and we only need to consider the first year (t is also 1), so the formula simplifies to A = P(1 + r). For the provided question, we have P = $10,500 and r = 0.11 (11 percent expressed as a decimal).
Therefore, the interest paid in the first year is calculated as follows:
- Initial calculation: Interest = P * r = $10,500 * 0.11 = $1,155
The final answer is that the interest paid in the first year is $1,155. This is a two-line explanation in 300 words or less, providing a clear and concise method to arrive at this conclusion.