Question

bruce takes out a personal loan of $1,000 to go on a trip to florida. his loan has an annual compound interest rate of 10%. the loan compounds once each year. when you calculate bruces debt, be sure to use the formula for annual compound interest. $a = p(1+\frac{r}{n})^{nt}$ bruce borrowed $1,000 for his trip. if bruce waits for five years to begin paying back his loan, how much will he owe? $1,251.10 $1,310.21 $1,610.51 $1,810.71

Explanation:

Step1: Identify values

$P = 1000$, $r = 0.10$ (10% as decimal), $n = 1$ (compounds annually), $t = 5$ (years).

Step2: Plug into formula

Use $A = P(1+\frac{r}{n})^{nt}$. Substitute values: $A = 1000(1+\frac{0.10}{1})^{1\times5}$.

Step3: Simplify exponent

Calculate exponent: $1\times5 = 5$. So, $A = 1000(1.10)^5$.

Step4: Compute $(1.10)^5$

$(1.10)^5 = 1.1\times1.1\times1.1\times1.1\times1.1 = 1.61051$.

Step5: Multiply by principal

$A = 1000\times1.61051 = 1610.51$.

Answer:

$1,610.51$ (corresponding to the option: $1,610.51$)