Question

You are looking at a one-year loan of $16,000. The interest rate is quoted as 11 percent plus two points. A point on a loan is simply 1 percent (one percentage point) of the loan amount. Quotes similar to this one are common with home mortgages. The interest rate quotation in this example requires the borrower to pay two points to the lender up front and repay the loan later with 11 percent interest.

What rate would you actually be paying here?

Answer 1

Loan Amount = $16,000

Up front payment = $16000 x 2 points = $16,000 x 2% = $320

Effective loan amount = Amount in hand on 1st day of loan = $16,000 - up front payment made = $ (16,000 - 320) = $15,680

Interest to be paid at the end of year 1 = 11% of $16000 = 11% x 16,000 = $1760

Rate of Interest on effective loan amount = Interest to be paid / Effective loan amount = 1760 / 15680 = 11.22% (approx.)

Note: We can't add the $320 up front payment to the interest amount, because the former is paid on the first day, and the latter is paid at the end of the year. For this reason, we simply reduce $320 from the loan amount to compute the effective loan amount.