Question

1.Assume you have just arranged a loan from your bank in the amount of $10,000. The bank will allow you to repay the loan with a lump sum payment of $11,500 in two years. No other payments will be made during this period. What is the implied EAR of this lending arrangement? (Do not round intermediate calculations. Round the final answer to 2 decimal places. Omit the % sign in your response. For example, an answer of 15.39% should be entered as 15.39.)

2. A bank wants to earn an EAR of 5%. The bank uses weekly compounding on all its loans. What interest rate is the bank required by law to report to potential borrows? (Do not round intermediate calculations. Round the final answer to 2 decimal places. Omit the % sign in your response. For example, an answer of 15.39% should be entered as 15.39.)

Answer 1

Question 1:

Calculation of EAR of the Loan

(1+EAR)^2= 1 + [($11,500 - $10,000) /$10,000]

(1+EAR)^2 = 1+15%

(1+ EAR)^2 = 1.15

1+EAR = 1.072380529

EAR = 0.072380529

Yearly EAR of the loan is 7.24%

Question 2:

EAR = 5%

n = Compoundings = 52 weeks

EAR = (1+r)^n - 1

5% = (1+r)^52 - 1

(1+r)^52 = 1.05

(1+r) = 1.0009387127

r = 0.0009387127

r = 0.09387127%

Annual Interest rate = 0.09387127% * 52 = 4.88130605618

Therefore, Interest rate is the bank required by law to report to potential borrows is 4.88% (APR)