Answer :
Answer:
The monthly payment is $2184.52
Explanation:
Given
[tex]Total\ Amount\ Spent\ = $220,000[/tex]
[tex]Amount\ Borrowed = 60\%[/tex]
[tex]Rate = 5.95\%[/tex]
[tex]Duration = 6\ years[/tex]
Required
[tex]Monthly\ Payment[/tex]
Firstly, the loan amount has to be calculated
The Question says; of the total amount spent, only 60% was borrowed;
So;
[tex]Loan = 60\%\ of\ 220,000[/tex]
[tex]Loan = 132,000[/tex]
The monthly payment can then be calculated using the following formula
[tex]Amount = P * \frac{r}{12} * \frac{(1 + \frac{r}{12})^n}{(1 + \frac{r}{12})^n - 1}[/tex]
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;
[tex]Amount = P * \frac{r}{12} * \frac{(1 + \frac{r}{12})^n}{(1 + \frac{r}{12})^n - 1}[/tex] becomes
[tex]Amount = 132,000 * \frac{0.0595}{12} * \frac{(1 + \frac{0.0595}{12})^{72}}{(1 + \frac{0.0595}{12})^{72} - 1}[/tex]
[tex]Amount = \frac{132,000*0.0595}{12} * \frac{(1 + \frac{0.0595}{12})^{72}}{(1 + \frac{0.0595}{12})^{72} - 1}[/tex]
[tex]Amount = \frac{132,000*0.0595}{12} * \frac{(1 + \frac{0.0595}{12})^{72}}{(1 + \frac{0.0595}{12})^{72} - 1}[/tex]
[tex]Amount = 654.5 * \frac{(1 + \frac{0.0595}{12})^{72}}{(1 + \frac{0.0595}{12})^{72} - 1}[/tex]
[tex]Amount = 654.5 * \frac{(\frac{12.0595}{12})^{72}}{(\frac{12.0595}{12})^{72} - 1}[/tex]
[tex]Amount = 654.5 * \frac{(1.0049583)^{72}}{(1.0049583)^{72} - 1}[/tex]
[tex]Amount = 654.5 * \frac{1.42777239524}{1.42777239524 - 1}[/tex]
[tex]Amount = 654.5 * \frac{1.42777239524}{0.42777239524}[/tex]
[tex]Amount = 2184.51925155[/tex]
[tex]Amount = 2184.52\ (Approximated)[/tex]
Hence, the monthly payment is $2184.52