Question

Julie is purchasing a home for $169,000.Her loan has been approved for a 30-year fixed-rate loan at 5 percent annual interest. She will pay 20 percent of the purchase price as a down payment. What is the total interest she will pay on her loan?

Answer 1

What is the total interest she will pay on her loan?

Answer 2

The total interest she will pay on her loan is $ 126080.80

Explanation:

Given : Julie is purchasing a home for $169,000.

She will pay 20 percent of the purchase price as a down payment.

So, 20% of $169,000 is given as ,

`169000\cdot(20)/(100)=33800`

Thus, amount left to pay = 169,000 - 33800 = $ 135200

Now, Her loan has been approved for a 30-year fixed-rate loan at 5 percent annual interest.

So, Finding monthly payment using formula,

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

Where, PV = present amount

P = monthly payment

r is interest rate per period

n is time per period

Here, PV = 135200

time period = 30 × 12 = 360 months

Monthly interest rate = 5 % =
`(5)/(1200)`

Substitute, we have,

`P=(135200\cdot(5)/(1200))/(1-\left(1+(5)/(1200)\right)^(-\left(30\cdot12\right)))`

Simplify, we have,

P = 725.78

Thus, Monthly payment is $ 725.78

Thus, the value of loan after 30 years becomes,

`725.78\cdot30\cdot12=261280.8`

Total interest paid = Total loan amount after 30 years - present amount

Total interest paid = 261280.8 - 135200 = 126080.8

Thus, The total interest she will pay on her loan is $ 126080.80