Question

Max's Kennels spent $220,000 to refurbish its current facility. The firm borrowed 60 percent of the refurbishment cost at 5.95 percent interest for six years. What is the amount of each monthly payment?

Answer 1

Answer:

The monthly payment is $2184.52

Explanation:

Given

$Total\ Amount\ Spent\ = 220,000$

$Amount\ Borrowed = 60\%$

$Rate = 5.95\%$

$Duration = 6\ years$

Required

$Monthly\ Payment$

Firstly, the loan amount has to be calculated

The Question says; of the total amount spent, only 60% was borrowed;

So;

$Loan = 60\%\ of\ 220,000$

$Loan = 132,000$

The monthly payment can then be calculated using the following formula

$Amount = P * \frac{r}{12} * \frac{(1 + \frac{r}{12})^n}{(1 + \frac{r}{12})^n - 1}$

Where P = Loan Amount = 132,000

r = rate of payment = 5.95% = 0.0595

n = duration (in month)

n = 6 years

n = 6 * 12 months

n = 72 months;

Substitute the above parameters in the formula;

$Amount = P * \frac{r}{12} * \frac{(1 + \frac{r}{12})^n}{(1 + \frac{r}{12})^n - 1}$ becomes

$Amount = 132,000 * \frac{0.0595}{12} * \frac{(1 + \frac{0.0595}{12})^{72}}{(1 + \frac{0.0595}{12})^{72} - 1}$

$Amount = \frac{132,000*0.0595}{12} * \frac{(1 + \frac{0.0595}{12})^{72}}{(1 + \frac{0.0595}{12})^{72} - 1}$

$Amount = \frac{132,000*0.0595}{12} * \frac{(1 + \frac{0.0595}{12})^{72}}{(1 + \frac{0.0595}{12})^{72} - 1}$

$Amount = 654.5 * \frac{(1 + \frac{0.0595}{12})^{72}}{(1 + \frac{0.0595}{12})^{72} - 1}$

$Amount = 654.5 * \frac{(\frac{12.0595}{12})^{72}}{(\frac{12.0595}{12})^{72} - 1}$

$Amount = 654.5 * \frac{(1.0049583)^{72}}{(1.0049583)^{72} - 1}$

$Amount = 654.5 * \frac{1.42777239524}{1.42777239524 - 1}$

$Amount = 654.5 * \frac{1.42777239524}{0.42777239524}$

$Amount = 2184.51925155$

$Amount = 2184.52\ (Approximated)$

Hence, the monthly payment is $2184.52