Answer:
$1078.80 (nearest cent)
$198,368 (nearest dollar)
Step-by-step explanation:
Monthly Payment Formula
[tex]\sf PMT=\dfrac{Pi(1+i)^n}{(1+i)^n-1}[/tex]
where:
- PMT = monthly payment
- P = loan amount
- i = interest rate per month (in decimal form)
- n = term of the loan (in months)
Given:
- P = $190,000
- i = 5.5%/12 = 0.055/12
- n = 30 × 12 = 360 months
Substitute the given values into the formula:
[tex]\implies \sf PMT=\dfrac{190000 \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 =1078.799103...[/tex]
Therefore, the monthly mortgage payment is $1078.80 (nearest cent).
To calculate the total amount of interest paid over the lifetime of the loan:
[tex]\begin{aligned}\sf Total\:interest & = \sf PMT \cdot n-P\\& = \sf 1078.80 \cdot 360-190000\\& = \sf 388368-190000\\& = \sf 198368\end{aligned}[/tex]
Therefore, the total amount of interest paid over the lifetime of the loan is $198,368 (nearest dollar).
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