Given:
There are given the total amount to buy a home $182000.
Explanation:
From the given question, there are saying that the 15% as a down payment
Then,
The total amount that pays as a down payment.
So,
[tex]\begin{gathered} 182000\times15\%=182000\times0.15 \\ =27300 \end{gathered}[/tex]Then,
Subtract the above amount from the total amount:
So,
[tex]182000-27300=154700[/tex](a):
The total loan amount is $154700.
(b):
The total loan amount is 182000.
The total number of periods is 30.
The interest rate per period is 5%.
So,
For calculating the monthly payment:
Divide the given rate by 12 and multiply the given period by 12.
So,
[tex]\begin{gathered} r=5\%=0.05 \\ =\frac{0.05}{12} \\ =0.0041 \\ n=30 \\ =30\times12 \\ =360 \end{gathered}[/tex]Now,
From the formula:
[tex]\begin{gathered} A=\frac{P(r(1+r)^n}{((1+r)^n-1)} \\ A=\frac{154700(0.0041(1+0.0041)^{360}}{((1+0.0041)^{360}-1)} \\ A=802.85 \end{gathered}[/tex]Then,
Put the all values into the above formula:
So,
The monthly payment is $802.85.
Now,
(c):
If the interest rate is 6%:
Then,
[tex]\begin{gathered} A=\frac{P(r(1+r)^n)}{((1+r)^n-1)} \\ A=\frac{154700(0.005(1+0.005)^{360})}{((1+0.005)^{360}-1)} \\ A=\frac{154700(0.005(1.005)^{360})}{((1.005)^{360}-1)} \\ A=\frac{4658.46}{5.022} \\ A=927.61 \end{gathered}[/tex]Final answer:
Hence, the answer of part (a), (b), and (c) are :
(a): $154700.
(b): $802.85
(c): $927.61
