Studdy AI Logo
Math

QuestionRegina's car loan costs \$41,503 at 6.5\% interest on a \$24,200 car. How many years is the loan in Ad A?

Studdy Solution

STEP 1

Assumptions1. The final cost of the loan is \$41,503. The interest rate for the loan is6.5%
3. The original price of the car is \$24,2004. The interest is calculated as a one-time payment, not compounding annually5. The total cost of the loan includes both the original price of the car and the interest

STEP 2

First, we need to find the total interest amount on the loan. We can do this by subtracting the original price of the car from the final cost of the loan.
Interest=Final cost of the loan−Original price of the carInterest = Final\, cost\, of\, the\, loan - Original\, price\, of\, the\, car

STEP 3

Now, plug in the given values for the final cost of the loan and the original price of the car to calculate the interest.
Interest=$41,503−$24,200Interest = \$41,503 - \$24,200

STEP 4

Calculate the interest amount.
Interest=$41,503−$24,200=$17,303Interest = \$41,503 - \$24,200 = \$17,303

STEP 5

Now that we have the interest amount, we can find the total number of years for the loan. The formula for simple interest isInterest=Principal amounttimesInterest ratetimesTimeInterest = Principal\, amount \\times Interest\, rate \\times TimeWe can rearrange this formula to solve for timeTime=InterestPrincipal amounttimesInterest rateTime = \frac{Interest}{Principal\, amount \\times Interest\, rate}

STEP 6

Plug in the values for the interest, the principal amount (which is the original price of the car), and the interest rate to calculate the time.
Time=$17,303$24,200times6.5%Time = \frac{\$17,303}{\$24,200 \\times6.5\%}

STEP 7

Convert the percentage to a decimal value.
6.5%=0.0656.5\% =0.065Time=$17,303$24,200times0.065Time = \frac{\$17,303}{\$24,200 \\times0.065}

STEP 8

Calculate the time for the loan.
Time=$17,303$24,200times0.065=11 yearsTime = \frac{\$17,303}{\$24,200 \\times0.065} =11\, yearsRegina will be paying back the loan in Ad A over11 years.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord