an ice - cream store sells for $400,000 and an 11% down payment is made. a 20 - year mortgage at 3.9% is…

an ice - cream store sells for $400,000 and an 11% down payment is made. a 20 - year mortgage at 3.9% is obtained. do not round intermediate calculations. round your answers to two decimal places, if necessary. use the formula below as needed.\nm=\frac{pcdot\frac{r}{n}}{1-(1 + \frac{r}{n})^{-nt}}\npart 1 of 4\n(a) find the down payment.\nthe down payment is $44,000.\npart 2 of 4\n(b) find the amount of the mortgage.\nthe amount of the mortgage is $356,000.\npart: 2 / 4\npart 3 of 4\n(c) find the monthly payment.\nthe monthly payment is $.\ntry again

an ice - cream store sells for $400,000 and an 11% down payment is made. a 20 - year mortgage at 3.9% is obtained. do not round intermediate calculations. round your answers to two decimal places, if necessary. use the formula below as needed.\nm=\frac{pcdot\frac{r}{n}}{1-(1 + \frac{r}{n})^{-nt}}\npart 1 of 4\n(a) find the down payment.\nthe down payment is $44,000.\npart 2 of 4\n(b) find the amount of the mortgage.\nthe amount of the mortgage is $356,000.\npart: 2 / 4\npart 3 of 4\n(c) find the monthly payment.\nthe monthly payment is $.\ntry again

Answer

Explanation:

Step1: Identify the values

$P = 356000$ (amount of mortgage), $r=0.039$ (annual interest rate), $n = 12$ (number of payments per year), $t = 20$ (number of years).

Step2: Substitute values into formula

First, calculate the exponent $-nt=-12\times20=-240$, and $\frac{r}{n}=\frac{0.039}{12}=0.00325$. Then, $1+\frac{r}{n}=1 + 0.00325=1.00325$, and $(1+\frac{r}{n})^{-nt}=1.00325^{-240}$. Using a calculator, $1.00325^{-240}\approx0.45277$. Also, $P\times\frac{r}{n}=356000\times0.00325 = 1157$. Then, $1-(1+\frac{r}{n})^{-nt}=1 - 0.45277=0.54723$.

Step3: Calculate monthly payment $M$

$M=\frac{1157}{0.54723}\approx2114.21$.

Answer:

$2114.21$