Question

A family is thinking about buying a new house

costing 380 000$. They must pay 110 000$ down and the rest is to
be amortized over 25 years in equal monthly payments. If money
costs 7% compounded monthly
(A)What will their monthly payment be?
(B)What will be unpaid balance after 20 years?
(C)How much total interest will be paid over the 25 years?

Answer 1

a.) 1908.30

b.) 96373.15

c.)302491.15

unrounded answers below

Explanation:

The amount that is to be loaned out is 380000-110000=270000

The effective montly rate is .07/12=.005833333

a.)

`270000=x((1-(1+.005833333)^(-(25*12)))/(.005833333))=1908.303833`

b.)

use what is called the prospective method (the outstanding loan balance at time n is equal to the present value of the remaining payments)

`1908.303833((1-(1+.005833333)^(-(25*12-20*12)))/(.005833333))=96373.14775`

c.)

total paid= 1908.303833*12*25=572491.1499

amount of loan: 270000

Total interest paid:

572491.1499-270000=302491.1499