Question

You have just purchased a new warehouse. To finance the purchase, you’ve arranged for a 30-year mortgage loan for 80 percent of the $3,400,000 purchase price. The monthly payment on this loan will be $17,500. What is the APR on this loan? What is the EAR on this loan?

Answer 1

Purchase price = $3,400,000

Amount financed = 80% * Purchase price
Amount financed = 80% * $3,400,000
Amount financed = $2,720,000

Monthly payment = $17,500
Period = 30 years or 360 months

Let monthly interest rate be i%

$2,720,000 = $17,500 * PVIFA(i%, 360)

Using financial calculator:
N = 360
PV = -2720000
PMT = 17500
FV = 0

I = 0.556%

Monthly interest rate = 0.556%
Annual interest rate = 12 * 0.556%
Annual interest rate = 6.672% or 6.67%

Effective annual rate = (1 + Monthly interest rate)^12 - 1
Effective annual rate = (1 + 0.00556)^12 - 1
Effective annual rate = 1.0688 - 1
Effective annual rate = 0.0688 or 6.88%

So, APR and EAR on this loan are 6.67% and 6.88% respectively.