QuestionRegina's loan costs \$38,402 at 5.3\% interest for 9 years. What is the car's price in Ad B?

Studdy Solution

STEP 1

Assumptions1. The total cost of the loan is $38,402. The interest rate is5.3%
3. The term of the loan is9 years4. The interest is calculated as a one-time payment, not yearly compounding5. The price of the car is the principal amount of the loan

STEP 2

First, we need to find the interest amount on the loan. We can do this by multiplying the principal amount by the interest rate and the term of the loan.
$Interest = Principal\, amount \\times Interest\, rate \\times Term$

STEP 3

We know the total cost of the loan and the interest rate, but we don't know the principal amount. So, we need to rearrange the formula to solve for the principal amount.
$Principal\, amount = \frac{Total\, cost}{1 + (Interest\, rate \\times Term)}$

STEP 4

Now, plug in the given values for the total cost, interest rate, and term to calculate the principal amount.
$Principal\, amount = \frac{\$38,402}{1 + (.3\% \\times9)}$

STEP 5

Convert the percentage to a decimal value.
$5.3\% =0.053$ $Principal\, amount = \frac{\$38,402}{1 + (0.053 \\times9)}$

STEP 6

Calculate the value inside the parentheses.
$Principal\, amount = \frac{\$38,402}{1 +0.477}$

STEP 7

Calculate the denominator.
$Principal\, amount = \frac{\$38,402}{1.477}$

STEP 8

Calculate the principal amount, which is the price of the car.
$Principal\, amount = \frac{\$38,402}{1.477} = \$26,000$ The price of the car offered in Ad B is $26,000.

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