Question

You are looking at a one-year loan of $26,000. The interest rate is quoted as 11 percent plus two points. A point on a loan is 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? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
Interest rate %

Answer 1

the rate of interest is 13.27%

Step-by-step explanation:

The computation of the actual rate paid is shown below;

Present value is

= $26,000 - 2% of $26,000

= $26,000 - $520

= $25,480

The future value is

= $26,000 × (1 + 0.11)

= $28,860

Now as we know that

Future value = Present value × (1 + rate of interest)^number of years

$28,860 = $25,480 × (1 + rate of interest)

So, the rate of interest is 13.27%