You are looking at a oneyear loan of 13000 The interest rate

You are looking at a one-year loan of $13,000. The interest rate is quoted as 8.6 percent plus three points. A point on a loan is simply 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 8.6 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 What is the EAR for a one-year loan with a quoted interest rate of 11.6 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.) EAR Is your answer affected by the loan amount? O No O Yes

Solution

Question 1). Solution :- Calculation of interest rate :-

Amount = Principal * (1 + interest rate)^{Time period in years}

13000 * (1 + 0.086)¹ = 13000 * (1 - 0.03) * (1 + R)¹ (R denotes the interest rate.)

13000 * (1.086)¹ = 13000 * 0.97 * (1 + R)

14118 = 12610 (1 + R)

14118 / 12610 = (1 + R)

(1 + R) = 1.1196

R = 1.1196 - 1

R = 0.1196 i.e., 11.96 %

Conclusion :- Interest rate = 11.96 % (approx).

Question 2). Solution :- Interest rate on loan = 11.6 % + 2 % (Two points) = 13.6 % or 0.136

EAR = (1 + Interest rate on loan / Number of compounding period in year)^{Number of compounding period in year} - 1.

= (1 + 0.136 / 12)¹² - 1 (1 Year = 12 Months)

= (1 + 0.01133333)¹² - 1

= (1.01133333)¹² - 1

= 1.1448 - 1

= 0.1448 i.e., 14.48 %

Conclusion :- Effective annual rate (EAR) = 14.48 % (approx).

No, The answer of 14.48 % would not be affected by the amount of loan i.e., whatever be the amount of loan, Effective annual rate (EAR) will remain same only.