Question

A credit card had an ARP of 15.24% all last year and compounded interest daily. What was the credit card's effective interest rate last year?

a) 16.35%

b) 16.13%

c) 15.82%

d) 16.46%

Answer 1

The effective interest rate for a credit card with an APR of 15.24% compounded daily is 16.13%, corresponding to option b).

Step-by-step explanation:

To calculate the effective interest rate (EIR) for a credit card with a 15.24% APR that compounds interest daily, we use the formula for EIR:

EIR = (1 + i/n)^(n*t) - 1,

where:
i = annual nominal interest rate
n = number of compounding periods per year
t = number of years

In this scenario:
i = 15.24/100 = 0.1524
n = 365 (daily compounding)
t = 1

Let's plug in the values:

EIR = (1 + 0.1524/365)^(365*1) - 1
EIR = (1 + 0.000417808)^(365) - 1
EIR = 1.1613 - 1
EIR = 0.1613 or 16.13%

Therefore, the effective interest rate for this credit card last year was 16.13%, which corresponds to option b).