Question

Ms. Moore is purchasing a house and needs to finance a $150,000 mortgage from the bank with an annual percentage rate (APR) of 3.8% she is financing it over 30 years and making monthly payments. What is the total amount Ms. Moore will pay back to the bank (to the nearest dollars)?

Answer 1

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 $M.P=\frac{P(\frac{r}{n})}{1-(1+\frac{r}{n})^{-nt}}$ , 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 = $\frac{3.8}{100}$ = 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

∵ $M.P=\frac{150000(\frac{0.038}{12})}{1-(1+\frac{0.038}{12})^{-(12)(30)}}$

∴ $M.P=\frac{475}{1-(\frac{6019}{6000})^{-360}}$

∴ 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

#LearnwithBrainly