Question

First Bank offers personal loans at 7.6 percent compounded monthly. Second Bank offers similar loans at 7.75 percent compounded semi-annually. Which one of the following statements is correct concerning these loans?

Group of answer choices

• The First Bank loan has an effective rate of 7.67 percent.

• The Second Bank loan has an effective rate of 8.03 percent.

• The annual percentage rate for the Second Bank loans is 7.90 percent.

• Borrowers should prefer the loans offered by Second Bank.

• The First Bank offers the best deal on loans.

Answer 1

Given,

First bank rate = 7.6% or 0.076

Second bank rate = 7.75% or 0.0775

Solution :-

EAR of first bank = [1 + (first bank rate/12)]¹² - 1

= [1 + (0.076/12)]¹² - 1

= [1 + 0.0063333333]¹² - 1

= [1.0063333333]¹² - 1

= 1.0787 - 1 = 0.0787 or 7.87%

EAR of second bank = [1 + (second bank rate/2)]² - 1

= [1 + (0.0775/2)]² - 1

= [1 + 0.03875]² - 1

= [1.03875]² - 1

= 1.0790 - 1 = 0.0790 or 7.90%

EAR of first bank is lower than EAR of second bank.

"The First Bank offers the best deal on loans."