1. "You are opening an individual retirement account (IRA) that earns 6% interest compounded daily. You wish to make monthly deposits into the IRA. You also want to purchase a new car for $25,000. You plan to set aside $790 every month, which will be divided between your IRA and your car payment. You are considering between two options:
OPTION 1: Make a down payment of $5,200 on the vehicle and borrow $19,800 at an APR of 8.4%, compounded monthly for 4 years. During these 4 years, you will deposit what remains of the $790 in the IRA (i.e., you will deposit $790 minus your car payment). After the vehicle is paid off at the end of 4 years, you will deposit $790 a month into your IRA.
OPTION 2: Make a down payment of $5,200 on the vehicle and borrow $19,800 at an APR of 8.4%, compounded monthly for 11 years. During these 11 years, you will deposit what remains of the $790 in the IRA (i.e., you will deposit $790 minus your car payment). After the vehicle is paid off at the end of 11 years, you will deposit $790 a month into your IRA.
Your goal is to maximize the amount in your IRA at the end of 30 years. Enter the dollar value of the IRA corresponding to the best option."
2. Ms. Manifee would like to purchase a new condo for $98,000. She plans to make a down payment of $52,000 and to borrow the rest of the money from the bank. The bank charges an annual percentage rate of 4% compounded daily. She agrees to monthly payments to pay off the loan in 13 years. What is her monthly payment?"