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Say that you purchase a house for $212,000 by getting a mortgage for $190,000 and paying a $22,000 down payment. If you get a 30-year mortgage with an interest rate of 8 percent, what are the monthly payments? What would the loan balance be in ten years?

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Edufirst

Answer:

1) Monthly payments:

        [tex]Payment=\$1,394.15[/tex]

2) Balance in ten years:

       [tex]Balance=\$166,676.94[/tex]

Explanation:

1. What are the monthly payments?

The formula to compute the monthly payment of a loan is:

       [tex]Payment=Loan\times \dfrac{r(1+r)^n}{(1+r)^n-1}[/tex]

Where:

  • Payment is the monthly payment
  • r is the monthly interes rate: 8% / 12 = 0.08/12
  • n is the number of months: 12 × 30 = 360
  • Loan = $190,000

Substitute and compute:

        [tex]Payment=\$ 190,000\times \dfrac{r(1+(0.08/12))^{360}}{(1+(0.08/12))^{360}-1}[/tex]

        [tex]Payment=\$1,394.15[/tex]

2. What would the loan balance be in ten years?

There is a formula to calculate the balance in any number of years:

     [tex]Balance=Loan(1+r)^n-Payment\times \bigg[\dfrac{(1+r)^n-1}{r}\bigg][/tex]

Substitute with n = 10 × 12 and compute:

[tex]Balance=\$190,000(1+(0.08/12))^{(10\times 12)}-\$1,394.15\times \bigg[\dfrac{(1+(0.08/12))^{(10\times 12)}-1}{(0.08/12)}\bigg][/tex]

[tex]Balance=\$166,676.94[/tex]

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