The nominal (quoted) annual interest rate on an automobile loan is 10%. The effective annual rate of the loan is 10.47%. The frequency of compounding periods per year for the loan is closest to:
Calculate and interpret the effective annual rate, given the stated annual interest rate and the frequency of compounding. Solve time value of money problems for different frequencies of compounding:
B is correct. Use the formula for effective annual rate:
EAR = (1 + Periodic interest rate)m– 1.
Iteratively substitute the possible frequency of compounding until the EAR is 10.47%.
For weekly compounding, (1 + 0.10/52)52 – 1 = 0.10506 = 10.51%
For monthly compounding, (1 + 0.10/12)12 – 1 = 0.10471 = 10.47%
For quarterly compounding, (1 + 0.10/4)4 – 1 = 0.10381 = 10.38%
Thus, the correct answer is monthly compounding.