Question

Suppose that you borrow $10,000 for four years at 7% toward the purchase of a car. Use PMT=

What is the monthly payment

Answer 1

`~~~~~~~~~~~~ \textit{Amortized Loan Value} \\\\ pmt=P\left[ \cfrac{(r)/(n)}{1-\left( 1+ (r)/(n)\right)^(-nt)} \right]\implies pmt=P\left[ \cfrac{(r)/(n)}{1-\left((n)/(n+r)\right)^(nt)} \right]`

`\begin{cases} P= \begin{array}{llll} \textit{original amount deposited}\\ \end{array}\dotfill & \begin{array}{llll} 10000 \end{array}\\ pmt=\textit{periodic payments}\\ r=rate\to 7\%\to (7)/(100)\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &4 \end{cases}`

`pmt=10000\left[ \cfrac{(0.07)/(12)}{1-\left((12)/(12+0.07)\right)^(12 \cdot 4)} \right]\\\\\\ pmt \approx 10000\left[ \cfrac{0.00583}{0.24360} \right]\implies pmt \approx 239.46`

Answer 2

I apologize if I’m wrong I’m not great at math but I think the answer is 40,007