1-) You plan your future retirement. There are two options for you:

Case 1: Deposit $500 at the end of each quarter for the first 5 years. Then, no further deposits, but the money stays for the next 8 years.

Case 2: Nothing is done first 5 years. Then deposit $5.000 at the end of each year for the next 8 years.

Assume that you are offered an interest rate of 6% compounded quarterly and you choose Case 2. Was that a correct decision?

2-) You are going to buy a milling machine for your company. The company borrows money to make the purchase and the loan terms are 9% per year, compounding monthly while making quarterly payments for 10 years. The machine costs $50,000.

1. Compute the equivalent interest rate for the payment period.
2. Compute the effective interest rate per year.
3. Compute the quarterly payments.
4. After 12 quarters, we realize that it would be advantageous to pay off the entire machine at the end of the next quarter. How much do we owe?

3-) A $10,000 loan is to be repaid in monthly equal payments in 10 years with an annual effective interest rate of 19.56% charged against the unpaid balance. What principal remains to be paid after the third payment?