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You take out a home loan for $190,000. The interest on this loan is fixed at 5.5% compounded monthly for 30 years.

.

How much is your required monthly mortgage payment? $
Round to the nearest dollar

USING THE WHOLE DOLLAR AMOUNT CALCULATED AS THE MONTHLY MORTGAGE PAYMENT, Over the entire period of the loan, what is the total amount of your payments? $
Round to the nearest dollar

What is total amount of interest you pay over the lifetime of the loan (i.e. how much more are you paying above the amount you borrowed)? $
Round to the nearest dollar

Respuesta :

semsee45

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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