Final answer:
The parents' loan option with an 8% interest payment every six months has a lower effective annual rate (EAR) of approximately 8.16% compared to the credit card's EAR of approximately 16.08%. Among the bank account options, Option a is slightly better than a 5% per year EAR account, while Option b is worse and Option c is significantly better.
Step-by-step explanation:
- Comparing Interest Rates for Holiday Financing
To determine which financing option has the lower rate for an Easter holiday, we need to compare the effective annual rates (EAR) for both options. The credit card has a 15% APR compounded monthly, while the parents offer an 8% interest payment every six months.
For the credit card, the monthly interest rate is 15% divided by 12, or 1.25% per month. Compounding monthly, the EAR can be calculated using the formula (1 + 0.0125)12 - 1, which gives us an EAR of approximately 16.08%.
For the parents' loan, the interest is compounded semi-annually, so the EAR is (1 + 0.08/2)2 - 1, which gives us an EAR of approximately 8.16%.
The parents' loan has a lower EAR compared to the credit card.
- Comparing Bank Accounts:
To compare the different banking options to a 5% per year EAR account:
Option a: An account that pays 2.5% every six months for three years has an EAR of (1 + 0.025)2 - 1 = 5.06%.
Option b: An account that pays 7.5% every 18 months for three years has an EAR of (1 + 0.075)2/3 - 1 = 4.90%.
Option c: An account that pays 0.5% pe
Comparing these options, Option a has a slightly higher EAR than 5% per year, Option b has a lower EAR, and Option c has the highest EAR of all.