Question

You are looking at a one-year loan of $20,000. The interest rate is quoted as 12 percent plus 4 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 4 points to the lender up front and repay the loan later with 12 percent interest. What rate would you actually be paying here? Multiple Choice 18.33% 16.67% 15.00% 7.52% 12.00%

Answer 1

Answer: approximately 12%

Explanation:

Simple interest SI =PRT

P is the principal,

R is the rate,

T is time in months.

On a $20000 loan for a year at the rate of 12%

SI = 20000x0.12x12 = $28800

The four points upfront amounts to

0.04x20000 = $800

Total interest = 28800+800 = $29600

This total interest will come at a rate we'll get by substituting it into the formula as the simple interest and solve for the interest rate over a one year period

29600 = 200000xRx12

29600 = 240000R

R = 29600/240000 = 0.1233

= 0.1233x100% = 12.3%

Approximately 12%