Question

claire wants to take out a small personal loan to renovate her kitchen. she borrows $3,000. her loan has an annual compound interest rate of 15%. the loan compounds once each year. when you calculate claire’s debt, be sure to use the formula for annual compound interest. a = p(1 + \frac{r}{n})^{nt} if claire does not make any payments, how much will she owe after ten years? \bigcirc $12,136.67 \bigcirc $3,481.24 \bigcirc $6,090.90 \bigcirc $3,232.74

Explanation:

Step1: Identify values

Principal \( P = 3000 \), rate \( r = 0.15 \), compounding periods per year \( n = 1 \), time \( t = 10 \).

Step2: Apply compound interest formula

Use \( A = P(1 + \frac{r}{n})^{nt} \). Substitute values: \( A = 3000(1 + \frac{0.15}{1})^{1\times10} \).

Step3: Calculate exponent and base

Simplify \( (1 + 0.15)^{10} = 1.15^{10} \approx 4.045558 \).

Step4: Find total amount

Multiply by principal: \( A = 3000 \times 4.045558 \approx 12136.67 \).

Answer:

\$12,136.67