MATH 674.1 Written Assignment #1 Fall 2016 1. Emily wants to buy a new car for $25,300, including all fees and taxes. \"Now's a good time to buy,\" claims the salesman, \"we're offering 4 year loans at 5.9%. Even if you have the cash, you're better off borrowing.\" Emily is confused. The salesman goes on to explain the payment on the car loan would be $593.01, which means that total interest paid on the loan will be $3,164.48. By investing the $25,300 at current savings account rates of 3.5% (compounded monthly), Emily could generate interest of $3,796.00 which means she'd be $631.52 better off by investing her money in a savings account. (a) Verify the numbers in the second paragraph. (b) Is Emily really better off by borrowing the money for her new car? 1 MATH 674.1 Written Assignment #1 Fall 2016 2. John and Jane Smith have just received a quote for home, car and liability insurance. The annual premium amounts to $3,500. They are given the choice of paying i) the entire amount in advance, ii) $310 per month with the first and last month due in advance; or iii) $920 per quarter, payable on the first of every quarter. (a) Calculate the rates being charged for Options (ii) and (iii). (b) Suppose the Smiths have exactly $3,500 in the bank, and suppose they can either borrow or lend at 15% compounded monthly. What do you recommend? 2 MATH 674.1 Written Assignment #1 Fall 2016 3. A recent newspaper advertisement offered car buyers the opportunity to lease a new vehicle for $5,000 down plus $350 per month for 48 months. At the end of the 48 months, the car will be returned to the dealer. Alternatively, the same car could be purchased outright for $34,000. It is estimated that in 48 months, the car could be sold for $20,000. At what interest rate (compounded monthly) are these two options equivalent? 3