1. You work for a bank that requires 30-year mortgages to have an eective interest rate (EAR) of 6.676%. The mortgages have monthly payments (and monthly compound- ing).

   1. (a) What is the Annual Percentage Rate (APR) of these mortgages?

   2. (b) A customer closes a deal to purchase a $800,000 home with 20% down. Her first payment is one month from now. Ignoring taxes and insurance, what is her monthly payment?

2. Payday lending has seen regulatory and social scrutiny for charging high interest rates. Google and Facebook have even banned advertisement of payday loans on their web- sites. A typical payday loan might allow you to borrow $100 today in exchange for $110 in two weeks. Lets assume there are exactly 52 weeks in a year.

   (a) What is the APR?

   (b) What is the EAR?

3. You are seeking a loan to purchase a car. The banker oers a loan with an APR of 12.75%, compounded semiannually. Your rich uncle, Milburn Pennybags, says he will oer you a loan with a 12.5% APR, with interest payments due every month. What is the eective annual rate for each loan? Which is oering the better rate?

4. Suppose your bank account pays interest monthly with the interest rate quoted as an EAR of 5%.

(a) What is the equivalent monthly interest rate?

(b) If you have no money in the bank today, how much will you need to save at the end of each month to accumulate $100,000 in 10 years?

5. If you invest $3,000 at an annual interest rate of 10% compounded continuously, what is the final amount you will have in the account after 15 years?