Question

Regina is buying a new car. She sees two advertisements in the paper for the same car at two different prices from two different dealerships. Both dealers are offering a simple-interest loan for the price of the car. A photo of car includes two ads. Ad A shows the vehicle priced at twenty-four thousand two hundred dollars at six point five percent interest and an unknown number of years. Ad B shows an unknown price, at a five point three percent interest over nine years. Question 1 Part A Regina calculates that to buy the car in Ad A, the loan would ultimately cost her $41,503. Over how many years is the loan in Ad A to be paid back?

Answer 1

11 years

Explanation:

Given that:

Advert A:

Principal, p = $24,200

Interest rate, r = 6.5% = 6.5/100 = 0.065

Time, t =?

Total Repayment, A = $41,503

Using the relation :

A = p(1 + rt)

Plugging our values

41503 = 24200(1 + 0.065t)

41503 / 24200 = 1 + 0.065t

1.715 = 1 + 0.065t

1.715 - 1 = 0.065t

0.715 = 0.065t

t = 0.715 / 0.065

t = 11 years

Loan in Advert A will be paid back in 11 years

Answer 2

11 years

Explanation:

Given that:

Advert A:

Principal, p = $24,200

Interest rate, r = 6.5% = 6.5/100 = 0.065

Time, t =?

Total Repayment, A = $41,503

Using the relation :

A = p(1 + rt)

Plugging our values

41503 = 24200(1 + 0.065t)

41503 / 24200 = 1 + 0.065t

1.715 = 1 + 0.065t

1.715 - 1 = 0.065t

0.715 = 0.065t

t = 0.715 / 0.065

t = 11 years

Loan in Advert A will be paid back in 11 years