Example 1: John determines that to buy the car of his choice, he will need to finance $20,000 for 5 years at 10.8% compounded monthly (This is most commonly written as 10.8% APR ­ annual percentage rate ­ with monthly compounding assumed) . Determine the amount of his monthly payment.
Solution: “He will need to finance $20000” means that John needs to borrow $20000 to make this purchase. Since John is getting the money “today” and making payments in the future, the present value of the money is $20000 (PV = 20000). “The amount of his monthly payment” indicates that he will make equal payments in equal time so this is an example of a simple annuity.
The terms of the loan are for 5 years with monthly payments (N = 5*12). The annual rate of interest is 10.8% (I% = 10.8). The loan will be paid back at the end of the five years. That is, at the end of 5 years the value of the debt will be $0 (FV = 0). Interest and payments occur monthly so both P/Y and C/Y are 12. To compute the amount of each payment, move the cursor to the PMT line and keypress ae to determine the amount of the payment is $432.86. (The negative result is a consequence of the financial consideration of an expense as opposed to income and can be ignored.)
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Example 2:
Lauren estimates that she can afford a monthly car payment of $250. If the terms of the loan are 5 years at 12.4% compounded monthly, how much money can she afford to borrow?
Solution: Lauren is planning on making equal payments in equal time so this qualifies as a simple annuity. The terms of the loan are described: 12.4% compounded monthly for 5 years. The amount of each payment is known and, since the loan will be completely paid after the 5 years, future value is 0. What needs to be found is the amount Lauren can borrow today, that is, the present value. Enter the data into the TVM solver. (Although it is not required, setting the characteristic which is being determined equal to ­1 ­ in this case PV ­ helps to not confuse the user as to which value is to be found.)
ae to solve
Lauren can afford to borrow $11,137.29 under these terms.
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1. Qiao is ready to buy his first car. He decides on a late model Ford Mustang GT convertible. Research shows the manufacturer’s suggested retail price to be $24,040. After doing some bargaining with a local dealer, Qiao agrees to a price of $25,900, after taxes. Qiao gives the dealer a check for $2590 and finances the rest at 4 year loan at 6.93% APR. Determine the amount of Qiao’s monthly payment.
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2. Jenny decides to use her $5000 bonus check as a down payment on a 2006 Sea Doo Sportster SCIC Sport Boat <http://www.seadoo.com/en­
US/SportBoats/2006/Sportster.SCIC/Introduction.htm> . After taxes, the cost of the boat is $28,400. She finances the rest of the purchase at 9.7% APR for 10 years. Determine the amount of Jenny’s monthly payment.
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3. Xavier and Elise are ready to buy their first house. After shopping around, they decide to take a 30 year loan at 6% compounded monthly. The home they want to buy costs $150,000 and they are required to make a 10% down payment. How much do they need to finance? What is the amount of each payment?
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4. What would the payment be in problem 3 if the loan was taken for 25 years at 6.5%?
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5. Jamie is considering buying a new car. After studying her budget, she determines that she can afford a down payment of $2500 and a monthly payment of $325. The best available loan is for 5 years at 7.1% compounded monthly.
(a) What is the most Jamie can afford to borrow?
(b) After taxes and fees, what is the most Jamie can spend on her car?
(a)
(b) $16,374.11 + $2500 = $18,874.11 7
Example 4: Consider the example of Xavier and Elise from problem 3. They took a 30 year, $135000 loan at 6% APR. Their monthly payments were $809.40. In all likelihood, Xavier and Elise will have had pay raises, maybe a family, and decide they need a bigger house. Eight years after buying the house, they decide to sell it and buy a new house. How much money do they owe on their first home and what was their equity at the time the house is sold?
A timeline for the original loan looks like
After 8 years, Xavier and Elise have made 96 payments. They still have 264 to make on this loan. The timeline for this problem is
The present value of these 264 payments of $809.40 is $118493.67.
Xavier and Elise still owe $118, 493.67 on the loan. Their equity on the loan is $135000 ­ 118, 493.67 = $16,506.33.
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