Question

A loan of $2100 is to be repaid with quarterly payments for 9 years at 9.8% interest compounded quarterly. Calculate the quarterly payment.

Answer 1

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

`\bf ~~~~~~ \begin{cases} P= \begin{array}{llll} \textit{original amount deposited}\\ \end{array}\dotfill & \begin{array}{llll} 2100 \end{array}\\ pymt=\textit{periodic payments}\dotfill \\ r=rate\to 9.8\%\to (9.8)/(100)\dotfill &0.098\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &9 \end{cases}`

`\bf pymt=2100\left[ \cfrac{(0.098)/(4)}{1-\left( 1+ (0.098)/(4)\right)^(-4\cdot 9)} \right] \implies pymt=2100\left[ \cfrac{0.0245}{1-\left( 1.0245\right)^(-36)} \right] \\\\\\ pymt\approx 2100\left[ \cfrac{0.0245}{0.5816215} \right]\implies pymt\approx 2100(0.0421236) \\\\\\ pymt\approx 88.45956`