Question

You want to buy a $33,000 car. The company is offering a 5% interest rate for 60 months (5 years). What will your monthly payments be?

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} 33000 \end{array}\\ pymt=\textit{periodic payments}\\ r=rate\to 5\%\to (5)/(100)\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \stackrel{payments}{\textit{monthly, thus twelve}} \end{array}\dotfill &12\\ t=years\dotfill &5 \end{cases}`

`\bf pymt=33000\left[ \cfrac{(0.05)/(12)}{1-\left( 1+ (0.05)/(12)\right)^(-12\cdot 5)} \right] \\\\\\ pymt=33000\left[ \cfrac{0.0041\overline{6}}{1-\left( 1+ 0.0041\overline{6}\right)^(-12\cdot 5)} \right] \\\\\\ pymt\approx 33000\left[ \cfrac{0.0041\overline{6}}{1-0.779} \right]\implies pymt\approx 33000\left[ \cfrac{0.0041\overline{6}}{0.22} \right] \\\\\\ pymt\approx 33000(0.01887)\implies pymt\approx 622.75`

Answer 2

A = $41,250.00 total / 60 for monthly payment = $ 687.5

Explanation:

(I = A - P = $8,250.00)

Equation:

A = P(1 + rt)

Calculation:

First, converting R percent to r a decimal

r = R/100 = 5%/100 = 0.05 per year.

Solving our equation:

A = 33000(1 + (0.05 × 5)) = 41250

A = $41,250.00

The total amount accrued, principal plus interest, from simple interest on a principal of $33,000.00 at a rate of 5% per year for 5 years is $41,250.00.