Question

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?

Answer 1

1) Monthly payments:

`Payment=\$1,394.15`

2) Balance in ten years:

`Balance=\$166,676.94`

Step-by-step explanation:

1. What are the monthly payments?

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

`Payment=Loan* (r(1+r)^n)/((1+r)^n-1)`

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:

`Payment=\$ 190,000* (r(1+(0.08/12))^(360))/((1+(0.08/12))^(360)-1)`

`Payment=\$1,394.15`

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

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

`Balance=Loan(1+r)^n-Payment* \bigg[((1+r)^n-1)/(r)\bigg]`

Substitute with n = 10 × 12 and compute:

`Balance=\$190,000(1+(0.08/12))^((10* 12))-\$1,394.15* \bigg[((1+(0.08/12))^((10* 12))-1)/((0.08/12))\bigg]`

`Balance=\$166,676.94`