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Sagot :
Answer:
a) $153,850
b) $779.54
c) $873.54
Step-by-step explanation:
Part a)
[tex]\begin{aligned}\textsf{Loan amount}&=\textsf{Cost of property}-\textsf{Down payment}\\&=181000-(181000 \times 0.15)\\&=181000-27150\\&=153850\end{aligned}[/tex]
Therefore, the loan amount is $153,850.
Part b)
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Monthly Payment Formula}\\\\$PMT=\dfrac{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}}[/tex]
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:
[tex]\implies \sf PMT=\dfrac{153850 \cdot \frac{0.045}{12}\left(1+\frac{0.045}{12}\right)^{360}}{\left(1+\frac{0.045}{12}\right)^{360}-1}[/tex]
[tex]\implies \sf PMT=\dfrac{153850 \cdot 0.00375\left(1.00375\right)^{360}}{\left(1.00375\right)^{360}-1}[/tex]
[tex]\implies \sf PMT=779.5353492[/tex]
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:
[tex]\implies \sf PMT=\dfrac{153850 \cdot \frac{0.055}{12}\left(1+\frac{0.055}{12}\right)^{360}}{\left(1+\frac{0.055}{12}\right)^{360}-1}[/tex]
[tex]\implies \sf PMT=873.5433786[/tex]
Therefore, the monthly payments would be $873.54.
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