use the monthly - payment formula to answer the question. round your answer to two decimal places, if…

use the monthly - payment formula to answer the question. round your answer to two decimal places, if necessary. a supermarket building was purchased for $573,000. the down - payment was 20%. the balance was financed at 7.92% for 15 years. find the monthly payment. the monthly payment is $

use the monthly - payment formula to answer the question. round your answer to two decimal places, if necessary. a supermarket building was purchased for $573,000. the down - payment was 20%. the balance was financed at 7.92% for 15 years. find the monthly payment. the monthly payment is $

Answer

Explanation:

Step1: Calculate the loan amount

The purchase price is $573000$. The down - payment is 20% of $573000$, so the down - payment amount is $0.2\times573000 = 114600$. The loan amount $P$ (the balance) is $573000−114600=458400$.

Step2: Convert the annual interest rate and number of years to monthly values

The annual interest rate $r = 7.92%=0.0792$. The monthly interest rate $i=\frac{0.0792}{12}=0.0066$. The number of years $n = 15$ years, and the number of payments $m=15\times12 = 180$ months.

Step3: Use the monthly - payment formula

The monthly - payment formula is $M=\frac{P\times i\times(1 + i)^{m}}{(1 + i)^{m}-1}$. Substitute $P = 458400$, $i = 0.0066$, and $m = 180$ into the formula. First, calculate $(1 + i)^{m}=(1 + 0.0066)^{180}$. Let $x=(1 + 0.0066)^{180}$. Using the formula $a^{b}=e^{b\ln(a)}$, we have $x = e^{180\times\ln(1.0066)}\approx3.2077$. Then, $M=\frac{458400\times0.0066\times3.2077}{3.2077 - 1}$. $458400\times0.0066\times3.2077=458400\times0.02117082 = 9700.28748$. $3.2077−1 = 2.2077$. $M=\frac{9700.28748}{2.2077}\approx4393.84$.

Answer:

$4393.84$