Question

You are looking at a one-year loan of $16,000. The interest rate is quoted as 7.8 percent plus three points. A point on a loan is 1 percent (one percentage point) of the loan amount. Quotes similar to this one are very common with home mortgages. The interest rate quotation in this example requires the borrower to pay three points to the lender up front and repay the loan later with 7.8 percent interest. a. 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.) b. What is the EAR for a one-year loan with a quoted interest rate of 10.8 percent plus two points? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

a.

Here,

Loan Amount = $16,000

Interest Rate = 7.8% + 3 Points

So,

Future Value(after 1 year) = (1 + 0.078)(16,000)

Future Value = $17,248

So borrower has to pay back $17,248 after 1 year

But,

With 3 points

Upfront cost = 0.03(16,000) = $480

Present Value of Loan = 16,000 - 480 = $15,520

So,

FV = PV(1 + r)^t

17248 = 15520(1 + r)

r = 11.34%

So,

Borrower is paying 11.34% effectively

b.

Quoted interest rate of 10.8 percent plus two points

So,

Future Value = (1 + 0.108)(16000)

Future Value = $17,728

Upfront Cost = 0.02(16000) = $320

Present Value = 16,000 - 320 = $15,680

So,

17728 = 15680(1 + r)

r = 13.06%

So,

Borrower is paying 13.06% effectively.