MTH 120 - Calculating Car Loans

MTH 120 - Calculating Car Loans - What What is the APR at a...

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Unformatted text preview: What What is the APR at a car dealership that will sell you a used car for $8,322 with $322 down and 60 monthly payments of $164.90? (Round your answer to the nearest tenth.) = , To To use the APR formula, we need to know N, the number of equal addpayments made at equal time intervals, and r, the add-on interest rate. . = − If the price is $8,322 and you make a $322 down payment, you will need to borrow is $8,000, i.e., $8,322 – $322; therefore… − t=5 A = P(1 + rt) ∙ (+∙) =, = ∙ = , … ) , ! + = − 60 We know from the word problem that the length of the loan is 60 months or 5 years; therefore… us Now, let find r using the Future Value Formula for Simple Interest… ) − P = $8,000 A = $9,894 (+ − . To find r, we need to know A, P and t… , (+ : ) Since P + I = $164.90 × 60 and A = P + I, we now know… =, So So we do not introduce any rounding errors, let's not do any of the math yet… We know from the word problem that N = 60; however, we need to Interest calculate r using the Future Value Formula for Simple Interest: We also know from the word problem that after making 60 monthly payments of $164.90, you will have paid off the loan, i.e., paid back the principal or amount borrowed, P, and interest, I. , divide Let’s divide both sides of the equation by 8,000… = + =(+ ( + ∙ )⟹ =, = − = Now, Now, let’s use our calculator to find r… ( − )÷ ÷ =. =. % Since we now know r, we can use the APR formula and our calculator to find the APR… = × + ×. =.% = × ÷( ×. + + )= . % … %; ,… ...
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This note was uploaded on 02/29/2012 for the course MATH 120 taught by Professor Adjunct during the Fall '11 term at Northern Virginia Community College.

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