Question

You take out a home loan for $160,073. The interest on this loan is 'fixed' at 6.2% compounded monthly for 30 years. How much is your required monthly mortgage payment?

a) $1,016.47

b) $966.80

c) $1,232.15

d) $1,074.89

Answer 1

The required monthly mortgage payment is $1,016.47.

thus correct option is a) $1,016.47

Step-by-step explanation:

To determine the monthly mortgage payment, you can use the formula for an amortizing loan, known as the loan amortization formula:

`\[ P = (r \cdot PV)/(1 - (1 + r)^(-n)) \]`

Where:

- ( P ) is the monthly payment

- ( PV ) is the present value or loan amount ($160,073 in this case)

- ( r ) is the monthly interest rate

- ( n ) is the total number of payments (30 years * 12 months = 360 payments)

First, convert the annual interest rate to a monthly rate:

`\[ r = (6.2\%)/(12 * 100) = 0.005167 \]`

Substitute the values into the formula:

`\[ P = (0.005167 * 160073)/(1 - (1 + 0.005167)^(-360)) \]`

Calculating this gives us a monthly payment of approximately $1,016.47, which aligns with option a). This calculation assumes fixed monthly payments over the entire loan term to pay off both the principal and interest.