The total interest she will pay on her loan is $ 126080.80
Step-by-step 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\frac{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=\frac{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 % = \frac{5}{1200}
Substitute, we have,
P=\frac{135200\cdot\frac{5}{1200}}{1-\left(1+\frac{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
