The total amount Ms. Moore will pay back to the bank is $251,617
Step-by-step explanation:
The formula of the monthly payment is [tex]M.P=\frac{P(\frac{r}{n})}{1-(1+\frac{r}{n})^{-nt}}[/tex] , where
- P is the loan amount
- r is the annual rate in decimal
- n is the number of periods per year
- t is the number of years
∵ Ms. Moore is purchasing a house and needs to finance a
$150,000 mortgage from the bank
∴ P = 150,000
∵ The annual percentage rate (APR) of 3.8%
∴ r = [tex]\frac{3.8}{100}[/tex] = 0.038
∵ She is financing it over 30 years and making monthly payments
∴ n = 12
∴ t = 30
- Let us substitute all of these numbers in the formula above
to find her monthly payment
∵ [tex]M.P=\frac{150000(\frac{0.038}{12})}{1-(1+\frac{0.038}{12})^{-(12)(30)}}[/tex]
∴ [tex]M.P=\frac{475}{1-(\frac{6019}{6000})^{-360}}[/tex]
∴ M.P = 698.936
∴ Her monthly payment is $698.936
Now multiply her monthly payment by the number of months in 30 years to find the total amount she will pay back to the bank
∵ 1 year = 12 months
∴ 30 years = 30 × 12 = 360
∴ Her total payments = 698.936 × 360
∴ Her total payments = 251,616.97
- Round it to the nearest dollar
∴ Her total payments = 251,617 dollars
The total amount Ms. Moore will pay back to the bank is $251,617
Learn more:
You can learn more about the mortgage in brainly.com/question/2485860
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