Question

16. Suppose we borrow from a credit card company at an APR of 24%, compounded monthly. What is the EAR on this loan?

      A. 26.0%

B. 27.1%

C. 26.8%

D. 27.8%

17. Related to the previous question, what is the EAR on this loan if compounded daily.

      A. 26.8%

      B. 28.6%

      C. 27.1%

      D. 27.9%

20. An investor buys 100 shares of a stock at $200 per share on 45% margin. The stock goes to $230. Ignoring all costs of transacting, the percentage return on the investor’s equity is

      A. 16.7%

      B. 33.3%

      C. 15%

      D. 27.3%

Answer 1

16.

Answer: C

EAR = {(1 + APR/m)^m} – 1

         = {(1 + 0.24/12)^12} – 1

         = {1.02^12} – 1

         = 1.268241 – 1

         = 0.268241

This is to be multiplied by 100 in order to get it in the percentage form; (0.268241 × 100 =) 26.8241% or rounded to 26.8%.

17.

Answer: C

EAR = {(1 + APR/d)^d} – 1

         = {(1 + 0.24/365)^365} – 1

         = {1.000657^365} – 1

         = 1.270901 – 1

         = 0.270901

This is to be multiplied by 100 in order to get it in the percentage form; (0.270901 × 100 =) 27.0901% or rounded to 27.1%.

20.

Answer: B

Total cost price = 100 shares × $200 = $20,000

Since the margin is 45%, the actual payment is (20,000 × 45% =) $9,000.

Total market price = 100 shares × $230 = $23,000

Gain = Total market price – total cost price = 23,000 – 20,000 = $3,000

Required return = (Gain / Actual payment) × 100

                            = (3,000 / 9,000) × 100

                            = (3 / 9) × 100

                            = 300 / 9

                            = 33.3%