Question

1. Two credit cards both state an APR of 20%. First National Bank’s card charges 1.667% compounded monthly. First United Bank’s card charges 10% compounded semiannually (twice a year). Given these APR’s, what are the effective annual rates charged by these two credit cards?

2. You want to buy a new house, but you are not sure what you can afford. What is the monthly payment for a 30 year loan with a 5.25% APR if the loan is for $290,000?
3. You want to know if you can afford a slightly more expensive house. What is the monthly payment for a 30 year loan with a 5.25% APR if the loan is for $325,000?

Answer 1

The effective annual rates for the credit cards are 21.94% and 21% when compounded monthly and semiannually, respectively. For a $290,000 and $325,000 house loan at a 5.25% APR over 30 years, the monthly payments would be $1,602.41 and $1,796.18, respectively.

Step-by-step explanation:

Understanding Credit Card APR and Loan Payments

The first question involves calculating the effective annual rates (EAR) for two credit cards offering 20% APR. The calculation involves different compounding periods for each card. Compounding monthly, First National Bank's card has an EAR of
(1 + 0.20/12)^(12) - 1 = 21.94%, and First United Bank's card, which compounds semiannually, has an EAR of (1 + 0.20/2)^(2) - 1 = 21%. As for the loan payment calculations for a 30-year mortgage at a 5.25% APR, the monthly payments would differ based on the principal amounts of $290,000 and $325,000.

To calculate the monthly payment for a 30-year loan at 5.25% APR, we would use the loan payment formula with the given nominal interest rate. For a $290,000 loan, the formula provides a monthly payment of $1,602.41. If the loan amount increases to $325,000, the monthly payment correspondingly increases to $1,796.18 at the same interest rate and term.