Question

When purchasing a $260,000 house, a borrower is comparing two loan alternatives. The first loan is a 90% loan at 8.5% for 25 years. The second loan is an 85% loan for 7.75% over 15 years. Both have monthly payments and the property is expected to be held over the life of the loan. What is the incremental cost of borrowing the extra money?

could you please show the work

Answer 1

Solution:

To find the incremental cost of borrowing the extra money,we should calculate the total payment under both loan

a)Calculation of total payment under 90% Loan amount

Loan Amount=$260,000*90%=$234,000

Monthly interest rate(r)=8.50/12=0.71% or 0.0071

No. of payment(n)=25*12=300

Monthly Payment=Loan Amount[r(1+r)^n/((1+r)^n-1)]

=$234000[0.0071(1+0.0071)^300/((1+0.0071)^300-1)]

=$1884.23

Total payment=Monthly payment*No. of payment

=$1884.23*300

=$565,269

Interest=$565,269-$$234,000

=$331,269

b)Calculation of total payment under 85% Loan amount

Loan amount=$260,000*85%=$221,000

Monthly interest rate(r)=7.75%/12=0.65% or 0.0065

No. of payment(n)=15*12=180

Monthly Payment=Loan Amount[r(1+r)^n/((1+r)^n-1)]

=$221,000[0.0065*(1+0.0065)^180/(1+0.0065)^180-1]

=$2080.22

Total payment=Monthly payment*No. of payment

=$2080.22*180

=$374,439.60

Interest=$374,439.60-$221,000

=$153,439.60

c)Thus,incremental cost of borrowing the extra money is;

=Interest under 90% loan amount-Interest under 85% Loan amount

=$331,269-$153,439.60

=$177,829.40