For example, suppose you negotiate a deal to purchase a new car for $19,055. You have a down payment and your old car to trade-in, and you qualify for a customer cash rebate. You plan to finance the rest of the cost with an auto loan.
Some states don’t allow a deduction of sales tax on trade-ins; you must pay tax on the total cost. For the example, suppose your state charges 7 percent sales tax and an additional $200 for tags and title fees. The sales tax would be $19,055∗. 07=$1,335{\displaystyle $19,055*. 07=$1,335}. The cost of the car would now be $20,590 ($19,055+$1,335+$200=$20,590){\displaystyle ($19,055+$1,335+$200=$20,590)}.
The dealer offers you $3,000 for your trade-in. This brings the cost of the car down to $17,590 ($20,590−$3,000=$17,590){\displaystyle ($20,590-$3,000=$17,590)}.
The dealer charges you $500 in destination and vehicle preparation fees. This brings the cost of the car to $18,090 ($17,590+$500=$18,090){\displaystyle ($17,590+$500=$18,090)}.
Typical rebates include customer cash for brand loyalty and dealer cash that may be passed along to the customer. Common incentives include low annual percentage rate (APR) financing for customers with excellent credit and special lease programs. You qualify for a brand loyalty rebate of $1,000. The cost of the car is now $17,090 ($18,090−$1,000=$17,090){\displaystyle ($18,090-$1,000=$17,090)}.
Your down payment is $2,000. This brings the total cost of the car down to $15,090 ($17,090−$2,000=$15,090){\displaystyle ($17,090-$2,000=$15,090)}. The amount you need to finance, or borrow, is $15,090.
The monthly payments remain the same, but the interest piece of the payment decreases and the principal piece increases over the course of the loan.
Use the formula A=P∗(r(1+r)n)/((1+r)n−1){\displaystyle A=P*(r(1+r)^{n})/((1+r)^{n}-1)}. A = the monthly payment. P = the principal r = the interest rate per month, which equals the annual interest rate divided by 12 n = the total number of months
Calculate the interest rate per month. The annual interest rate is 7 percent. Divide this by 12 to get the monthly interest rate. The monthly interest rate is 0. 583 percent (7/12=. 5833){\displaystyle (7/12=. 5833)} A=15,090∗(. 00583(1+. 00583)48)/(1+. 00583)48−1{\displaystyle A=15,090*(. 00583(1+. 00583)^{48})/(1+. 00583)^{48}-1}. A=15,090∗(. 0077/. 3218){\displaystyle A=15,090*(. 0077/. 3218)}. A=15,090∗. 02393=361. 07{\displaystyle A=15,090*. 02393=361. 07} Your monthly payment will be $361. 07
Multiply the length of the loan in years by 12. You want to calculate monthly payments, not annual payments, so you’ll need the total number of months throughout the life of the loan. For example, if the loan is for four years, then the number of months is 4 * 12, or 48. Since you want to pay off the loan completely, the future value of the loan will be 0. This means that you won’t owe any more money at the end of the payment stream.
Rate Number of Payments Present Value Future Value
7. 00% 48 15,090 0
Type “=PMT(“ and click on the cell with 7. 00% so “B1” appears after the left parentheses. Type “/12,” (including the comma). Remember, you’re dividing by 12 because you’re calculating the interest rate on a monthly basis and the interest rate you were given is on an annual basis. Click on the cell with 48 to see “B2” appear. Type a comma after “B2” and click on the cell with 15,090 to see “B3” appear. Type a comma after “B3” and click on the cell with 0 to see “B4” appear. Type a right parenthesis at the end to complete the formula.
