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 addon 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.
 Fall '11
 Adjunct
 Math

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