Question

A borrower can obtain an 80 percent loan with an 8% interest rate and monthly payments. The loan is to be fully amortized over 25 years. Alternatively, he could obtain a 90 percent loan at an 8.5% rate with the same loan term. The borrower plans to own the property for the entire loan term. What is the incremental cost (%) of borrowing the additional funds? (Hint: the dollar amount of the loan does not affect the answer)

Answer 1

Answer:

19.5% increase in monthly repayment

Explanation:

The two scenarios are analysed to find the monthly repayment that will be due on them on a monthly basis for the 25 year repayment period.

The monthly repayment (A) is computed thus, given a principal amount (P), a monthly rate of interest (r), and the number of months in 25 years (n = 25*12 = 300):

$A=\frac{Pr}{1-(1+r)^{-n} }$

Scenario 1: 80% loan, with 8% annual rate for 25 years

P = 80; r = 8%/12 = 0.6667; n = 300 months

$A=\frac{80*0.6667}{1-(1.6667)^{-300} }$

= 53.336

Scenario 2: 90% loan, with 8.5% annual rate for 25 years

P = 90; r = 8.5%/12 = 0.7083; n = 300 months

$A=\frac{90*0.7083}{1-(1.7083)^{-300} }$

= 63.747

Thus, the monthly payment will increase by $\frac{63.747}{53.336}$ = 19.5% monthly due additional funds borrowed.