Question

You want to buy a $181,000 home. You plan to pay 15% as a down payment, and take out a 30 year fixed loan for the rest.

Round all answers to the nearest cent as needed.

a) How much is the loan amount going to be?
$


b) What will your monthly payments be if the interest rate is 4.5%?
$


c) What will your monthly payments be if the interest rate is 5.5%?
$
Submit QuestionQuestion 4

Answer 1

a) $153,850

b) $779.54

c) $873.54

Explanation:

Part a)

`\begin{aligned}\textsf{Loan amount}&=\textsf{Cost of property}-\textsf{Down payment}\\&=181000-(181000 * 0.15)\\&=181000-27150\\&=153850\end{aligned}`

Therefore, the loan amount is $153,850.

Part b)

`\boxed{\begin{minipage}{8.5 cm}\underline{Monthly Payment Formula}\\\\$PMT=(Pi\left(1+i\right)^n)/(\left(1+i\right)^n-1)$\\\\where:\\\\ \phantom{ww}$\bullet$ $P =$ loan amount \\\phantom{ww}$\bullet$ $i =$ interest rate per month (in decimal form) \\\phantom{ww}$\bullet$ $n =$ term of the loan (in months) \\\end{minipage}}`

Given:

• P = $153,850
• i = 0.045 per year = 0.045/12 per month
• n = 30 years = 360 months

Substitute the given values into the Monthly Payment formula and solve for PMT:

`\implies \sf PMT=(153850 \cdot (0.045)/(12)\left(1+(0.045)/(12)\right)^(360))/(\left(1+(0.045)/(12)\right)^(360)-1)`

`\implies \sf PMT=(153850 \cdot 0.00375\left(1.00375\right)^(360))/(\left(1.00375\right)^(360)-1)`

`\implies \sf PMT=779.5353492`

Therefore, the monthly payments would be $779.54.

Part c)

Given:

• P = $153,850
• i = 0.055 per year = 0.055/12 per month
• n = 30 years = 360 months

Substitute the given values into the Monthly Payment formula and solve for PMT:

`\implies \sf PMT=(153850 \cdot (0.055)/(12)\left(1+(0.055)/(12)\right)^(360))/(\left(1+(0.055)/(12)\right)^(360)-1)`

`\implies \sf PMT=873.5433786`

Therefore, the monthly payments would be $873.54.