Question

A borrower is offered a mortgage loan for $100,000 with an interest rate of 10% and a 30-year amortization period with monthly payments. The origination fee is 1% of the loan and the lender charges two discount points. What is the effective interest rate?

Answer 1

Calculate the monthly payment:

PV = 100000

Rate = 10%/12

Nper = 30 * 12 = 360

FV = 0

Monthly payment can be calculated by using the following excel formula:

=PMT(rate,nper,pv,fv)

=PMT(10%/12,360,-100000,0)

= $877.57

Calculation of effective rate:

Actual loan = $100,000 - ($100,000 * 1%) - ($100,000 - 0.02) = $97000

Nper = 360

PMT = 877.57

Effective rate can be calculated by using the following excel formula:

=RATE(nper,pmt,pv,fv)*12

=RATE(360,877.57,-97000,0)*12

= 10.37%

Effective rate = 10.37%