Credit Card Ear
1. Stating the problem:
a) Calculate the effective annual interest rate (EAR) given a nominal annual interest rate of 21.9% compounded daily (365 times per year).
2. Formula for EAR with daily compounding:
$$EAR = \left(1 + \frac{r}{n}\right)^n - 1$$
where $r = 0.219$ (nominal rate), $n = 365$ (days per year).
3. Substitute values:
$$EAR = \left(1 + \frac{0.219}{365}\right)^{365} - 1$$
4. Calculate inside the parentheses:
$$1 + \frac{0.219}{365} = 1 + 0.0006 = 1.0006$$ (rounded)
5. Raise to power 365:
$$1.0006^{365} \approx 1.24495$$
6. Subtract 1 to get EAR:
$$EAR = 1.24495 - 1 = 0.24495$$
7. Convert to percentage:
$$0.24495 \times 100 = 24.495\% \approx 24.4\%$$
8. For part b):
The main drawback of using a credit card for cash advances is that interest starts accumulating immediately on the cash advance amount without any grace period, meaning Finn pays interest from the day he withdraws cash until he repays the balance fully.
9. For part c):
Since cash advances do not have a grace period, the effective interest rate on cash advances is effectively the same as the EAR calculated for purchases — 24.4% annually assuming daily compounding.
Final answers:
a) EAR = 24.4%
b) Interest on cash advances starts immediately with no grace period
c) EAR on cash advances = 24.4%