Question

A property costs $225,000. A borrower can obtain an 80% loan with an 10% interest rate and monthly payments. The loan is to be fully amortized over 20 years. Alternatively he could obtain a 90% loan at an 10.25% interest 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?

Answer 1

80% loan

Loan amount = cost of property * LTV = $225,000 * 80% = $180,000

Monthly loan payment is calculated using PMT function in Excel :

rate = 10% / 12   (converting annual rate into monthly rate)

nper = 20*12 (30 year loan with 12 monthly payments each year)

pv = 180000 (loan amount)

PMT is calculated to be $1,737.04

Total amount paid over 20 years =  $1,737.04 * 20 * 12 = $416,889.35

Total interest paid over 20 years = $416,889.35 - $180,000 = $236,889.35

90% loan

Loan amount = cost of property * LTV = $225,000 * 90% = $202,500

Monthly loan payment is calculated using PMT function in Excel :

rate = 10.25% / 12   (converting annual rate into monthly rate)

nper = 20*12 (30 year loan with 12 monthly payments each year)

pv = 202500 (loan amount)

PMT is calculated to be $1,987.83

Total amount paid over 20 years =  $1,987.83 * 20 * 12 = $477,078.69

Total interest paid over 20 years = $477,078.69 - $202,500 = $274,578.69

Incremental cost of borrowing additional funds = difference in total interest paid

Incremental cost of borrowing additional funds = $274,578.69 - $236,889.35

Incremental cost of borrowing additional funds = $37,689.34