5. juliana is taking out an $8,700, 3 - year loan with an apr of 2.31%. what will be the monthly payment for…

5. juliana is taking out an $8,700, 3 - year loan with an apr of 2.31%. what will be the monthly payment for this loan? monthly payment formula m = monthly payment p = principal r = interest rate as decimal n = number of years $m=\frac{p(\frac{r}{12})(1 + \frac{r}{12})^{12t}}{(1+\frac{r}{12})^{12t}-1}$

5. juliana is taking out an $8,700, 3 - year loan with an apr of 2.31%. what will be the monthly payment for this loan? monthly payment formula m = monthly payment p = principal r = interest rate as decimal n = number of years $m=\frac{p(\frac{r}{12})(1 + \frac{r}{12})^{12t}}{(1+\frac{r}{12})^{12t}-1}$

Answer

Explanation:

Step1: Identify the values

$P = 8700$, $r=0.0231$, $t = 3$

Step2: Substitute values into formula

First, calculate the numerator: $P\left(\frac{r}{12}\right)\left(1 + \frac{r}{12}\right)^{12t}=8700\times\left(\frac{0.0231}{12}\right)\times\left(1+\frac{0.0231}{12}\right)^{12\times3}$ $=8700\times0.001925\times(1 + 0.001925)^{36}$ $=16.7475\times(1.001925)^{36}$ $(1.001925)^{36}\approx1.07177$ $16.7475\times1.07177\approx17.95$

Then, calculate the denominator: $\left(1+\frac{r}{12}\right)^{12t}-1=(1.001925)^{36}-1\approx1.07177 - 1=0.07177$

$M=\frac{17.95}{0.07177}\approx250.1$

Answer:

$250.1$