Question

You want to earn an EAR of 12.682%. Therefore, you would pick an investment with a quoted interest rate of _________ APR with monthly compounding:

A) 12.30%
B) 12.68%
C) 12.00%
D) 12.28%
E) None of the above

Answer 1

The correct option is C) 12.00%.

Explanation:

This can be calculated using the formula for calculating the effective annual rate (EAR) as follows:

EAR = ((1 + (i / n))^n) - 1 .............................(1)

Where;

EAR = effective annual rate = 12.682%, or 0.12682

i = annual percentage rate (APR) = ?

n = Number of compounding periods or months = 12

Substituting the values into equation (1) and solve for i, we have:

0.12682 = ((1 + (i / 12))^12) - 1

0.12682 + 1 = (1 + (i / 12))^12

1.12682 = (1 + (i / 12))^12

(1.12682)^(1/12) = (1 + (i / 12))^(12/12)

1.12682^0.0833333333333333 = 1 + (i / 12)

1.00999962428035 - 1 = i / 12

0.00999962428035 = i / 12

i = 0.00999962428035 * 12

i = 0.119995491364199, or 11.9995491364199%

Approximating to 2 decimal places, we have:

i = 12.00%

Therefore, the correct option is C) 12.00%.