Question

How much interest (to the nearest dollar) would be saved on the following loan if the home were financed for 15 rather than 30 years?

A $511,000 home bought with a 20% down payment and the balance financed for 30 years at 5.3%

Answer 1

Lets find installment amount and interest paid if loan is taken for 30 years

Amount of loan = Cost of home(1-down payment)

=511000(1-20%)

=511000(1-0.2)

=511000(0.8)

=408800 $

Installment = Loan / PFIFA(r%,n)

r % = interest rate = 5.3%

n = no of years = 30 years

PVIFA(r%,n) = [1-(1/(1+r)^n / r ]
PVIFA(5.3%,30) = [1-(1/(1+5.3%)^30 / 5.3%]
=[1-(1/(1+0.053)^30 / 0.053]
=[1-(1/(1.053)^30 / 0.053]
=[1-0.2124 / 0.053]
=0.7876/0.053
=14.8604

Thus Installment = 408800/14.8604

=27509.30 $

Thus total amount paid = Installment x no. of years

=27509.30 x 30

=825278.97 $

Thus interest paid = Total amount paid - Loan amount

=825278.97 - 408800

=416478.97 $

Lets find installment amount and interest paid if loan is taken for 15 years

Installment = Loan / PFIFA(r%,n)

r % = interest rate = 5.3%

n = no of years = 15 years

PVIFA(r%,n) = [1-(1/(1+r)^n / r ]
PVIFA(5.3%,15) = [1-(1/(1+5.3%)^15 / 5.3%]
=[1-(1/(1+0.053)^15 / 0.053]
=[1-(1/(1.053)^15 / 0.053]
=[1-0.4609 / 0.053]
=0.5391/0.053
=10.1723

Thus Installment = 408800/10.1723

=40187.39 $

Thus total amount paid = Installment x no. of years

=40187.39 x 15

=602810.89 $

Thus interest paid = Total amount paid - Loan amount

=602810.89 - 408800

=194010.89 $

Thus 222468 $ ($416478.97 - $ 194010.89) would be saved on the loan if the home were financed for 15 rather than 30 years