Question

our friend purchases a $185,000 house. He is able to make a 15% down payment. The bank will give him a 30-year loan with a 3.5% APR.

How much money will he borrow for his mortgage?

$ (round to the nearest dollar)

What would his monthly payment be?

$ (round to the nearest cent)

How much interest will your friend pay over 30 years of his loan?

$ (round to the nearest cent)

Answer 1

Answer:

Given,

The value of the house = $ 185,000,

Percentage of down payment = 15%,

(i) So, the borrowed amount = 185,000 - 15% of 185,000

$=185000-\frac{15\times 185000}{100}$

$=185000-\frac{2775000}{100}$

$=185000-27750$

$=\ 157250$

(ii) Since, the monthly payment formula of a loan is,

$P=\frac{PV\times r}{1-(1+r)^{-n}}$

Where,

PV = present value of the loan ( or borrowed amount )

r = rate per month,

n = number of months,

Here, PV = $ 157250,

APR = 3.5% = 0.035 ⇒ r = $\frac{0.035}{12}$ ( 1 year = 12 months )

Time = 30 years, ⇒ n = 360 months,

Hence, the monthly payment would be,

$P=\frac{157250\times \frac{0.035}{12}}{1-(1+\frac{0.035}{12})^{-360}}$

$=706.122771579$    ( by graphing calculator ),

$\approx \ 706.12$

(iii) Interest = Total amount paid - borrowed amount

= 706.122771579 × 360 - 157250

= 96954.1977684

≈ $ 96954. 20