Question

(See Example 7) The Hiles family has obtained a house loan of $48,000 for 25 years at 4.5% interest. The monthly payments are $266.80. (Round your answers to two decimal places.)

(a) What is the balance of their loan after 1 year?
$

(b) What is the balance of their loan after 2 years?
$

(c) What is their equity after 1 and 2 years?

1 yr	$
2 yr	$

Compare the total payments made over 1 year with the equity after 1 year.

The total payments made over the one-year period was $  , as compared to $  of equity after the one-year period.

Compare the total payments made over 2 years with the equity after 2 years.

The total payments made over the two-year period was $  , as compared to $  of equity after the two-year period.

Answer 1

Solution:we have Loan(PV) =$48000

Monthly payment(P) =$266.80

Number of payment due after1 year (n) =(25-1) ×12=288

Rate of interest(i)=4.5%/12=0.00375 monthly

a) Now, to calculate Balance loan amount, using:

PV=P[1-(1+i)^-n]/i

or, PV=266.80[1-(1+0.00375)^-288]/0.00375

=266.80[1-(1.00375)^-288/0.00375

=266.80[1-0.34028]/0.00375

=266.80*0.6597/0.00375

=$46936.72

b) Now, Monthly payment (P) =266.80

Number of payment after 2 years(n) =(25-2) ×12=276

Rate of interest(i)=0.00375

Now, to calculate laon balance after 2 year, using:

PV=P[1-(1+i)^-n]/i

or, PV=266.80[1-(1+0.00375)^-276]/0.00375

=266.80[1-0.3559]/0.00375

=266.80×0.64408/0.00375

=$45824.52