you borrowed some money on a short - term loan for 2 years at 11% which was compounded monthly. the total…

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the final amount, $P$ is the principal amount (the initial amount borrowed), $r$ is the annual interest rate (in decimal form), $n$ is the number of times interest is compounded per year, and $t$ is the number of years. We are given that $A=$72693.90$, $r = 0.11$ (since $11%=0.11$), $n = 12$ (compounded monthly), and $t = 2$. We need to solve the formula for $P$: $P=\frac{A}{(1 +\frac{r}{n})^{nt}}$.

Step2: Substitute the values into the formula

First, calculate the exponent $nt$: $nt=12\times2 = 24$. Then, calculate the value inside the parentheses: $1+\frac{r}{n}=1+\frac{0.11}{12}\approx1 + 0.009167=1.009167$. Next, calculate $(1+\frac{r}{n})^{nt}=(1.009167)^{24}$. Using a calculator, $(1.009167)^{24}\approx1.244797$. Now, find $P$: $P=\frac{72693.90}{1.244797}\approx58400$.

Answer:

$58400$