the ramirez family bought a new dining room set from the local furniture store. they financed the purchase…

Explanation:

Step1: Calculate monthly interest rate

The annual interest rate $r = 4%=0.04$. The monthly interest rate $i=\frac{0.04}{12}$.

Step2: Identify number of periods

The loan is for $n = 36$ months.

Step3: Use loan - payment formula

The formula for the present - value of an ordinary annuity (derived from the sum of a finite geometric series) is $PV = PMT\times\frac{1-(1 + i)^{-n}}{i}$, where $PV$ is the present value of the loan, $PMT$ is the monthly payment, $i$ is the monthly interest rate, and $n$ is the number of periods. We want to solve for $PMT$. Rearranging the formula gives $PMT=\frac{PV\times i}{1-(1 + i)^{-n}}$. Substitute $PV = 3682$, $i=\frac{0.04}{12}$, and $n = 36$ into the formula: [ \begin{align*} i&=\frac{0.04}{12}\approx0.00333\ PMT&=\frac{3682\times0.00333}{1-(1 + 0.00333)^{-36}}\ (1 + 0.00333)^{-36}&=\frac{1}{(1.00333)^{36}}\ (1.00333)^{36}&\approx1.12727\ (1 + 0.00333)^{-36}&\approx\frac{1}{1.12727}\approx0.88717\ 1-(1 + 0.00333)^{-36}&=1 - 0.88717=0.11283\ 3682\times0.00333&=12.26106\ PMT&=\frac{12.26106}{0.11283}\approx108.71 \end{align*} ]

Answer:

A. $$108.71$