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# Applied Math 40S Slides May 3, 2007

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• 1. Kandi decided to quit smoking on her 18th birthday. She also decided to invest some of the money saved into a retirement fund that pays 7.5% per annum compounded monthly. If she pays \$20 per month, starting on her 18th birthday, and pays until her 60th birthday, how much money would she have in her retirement fund on her 60th birthday after making her final deposit?
• 2. Jeff bought a Chevy truck, and used his older Dodge truck as trade. The price of the Chevy was \$22 500, and the trade-in value of the Dodge was \$3200. How much did Jeff have to pay? Note: PST (7%) and GST (6%) have to be paid on new car purchases. On used cars only PST is paid.
• 3. Determine the monthly payment for a \$8250.00 loan with an interest rate of 8.9% compounded monthly if the loan is repaid in two years (24 monthly payments). Also determine the total cost of repaying the loan, and the amount of interest paid.
• 4. Leasing ... When you lease an item such as a car or computer, you are renting an item owned by the lessor. You, the lessee, must make monthly payments to pay for: • the depreciation of the item • the sales taxes on the amount of depreciation • the interest on the unpaid value of the item At the end of the lease, you either return the item to the lessor or buy it for the residual value (i.e., the estimate of the item's worth at lease end as determined by the lessor at the beginning of the lease).
• 5. Leasing continued ... When you lease a vehicle, you need to sign a lease agreement. This agreement specifies: • the initial value of the item • the buy out price at the end of the lease (which is the same as the residual value) • the down payment (if there is one) • any additional fees • the interest rate • the monthly payment. The lease agreement will also specify other terms or restrictions, such as what is reasonable use and care of the item. For example, a car lease will specify how many kilometres you can drive, and the fee per kilometre if you exceed this limit.
• 6. Trudy wants to buy a used Ford Mustang for \$16 000 plus tax. She has \$3 000 for a down payment and needs a loan to pay the rest. The bank charges 9% interest compunded monthly and the loan must be repaid in 3 years. What is the loan principal? How much are Trudy's monthly payments?
• 7. Jess wants to buy a 4 x 4 pickup truck for \$24 950.00 plus PST and GST at 7% each. She will use her present small car as a trade, and will receive \$5 200.00 trade-in value. She will make a \$3000 down payment, and pay for the balance of the cost of the vehicle with a loan. The loan interest rate is 8.75%, and must be repaid in 3 years. What are her monthly payments and what is the total cost of the truck?
• 8. Jess also looks at the option of leasing the vehicle for 3 years. the price is \$24 950.00 plus GST and PST at 7% each, and the residual value (i.e. the buyout price) is set at 48% of the new price, which is \$11 976.00. The down payment is \$2 250 and the interest rate is 8.75%. (a) What is Jess’ monthly (b) How much does Jess pay for the lease in total? lease payment? (c) If Jess decides to buy the truck at the end of the lease, and makes a 2 year loan at 8% to pay the buyout price, how much will she pay for the truck altogether?
• 9. Jess also looks at the option of leasing the vehicle for 3 years. the price is \$24 950.00 plus GST and PST at 7% each, and the residual value (i.e. the buyout price) is set at 48% of the new price, which is \$11 976.00. The down payment is \$2 250 and the interest rate is 8.75%. (a) What is Jess’ monthly (b) How much does Jess pay for the lease in total? lease payment? (c) If Jess decides to buy the truck at the end of the lease, and makes a 2 year loan at 8% to pay the buyout price, how much will she pay for the truck altogether?
• 10. Jess also looks at the option of leasing the vehicle for 3 years. the price is \$24 950.00 plus GST and PST at 7% each, and the residual value (i.e. the buyout price) is set at 48% of the new price, which is \$11 976.00. The down payment is \$2 250 and the interest rate is 8.75%. (c) If Jess decides to buy the truck at the end of the lease, and makes a 2 year loan at 8% to pay the buyout price, how much will she pay for the truck altogether?