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(b) (i) How much is to be paid as a deposit under this option? (1) (ii) Find the cost of the loan under Friendly Credit Terms

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IB Questionbank Mathematical Studies 3rd edition 1

1. Angela needs $4000 to pay for a car. She was given two options by the car seller.

Option A: Outright Loan

A loan of $4000 at a rate of 12% per annum compounded monthly.

(a) Find

(i) the cost of this loan for one year;

(2) (ii) the equivalent annual simple interest rate.

(2)

Option B: Friendly Credit Terms

A 25% deposit, followed by 12 equal monthly payments of $287.50.

(b) (i) How much is to be paid as a deposit under this option?

(1) (ii) Find the cost of the loan under Friendly Credit Terms.

(2)

(c) Give a reason why Angela might choose (i) Option A

(ii) Option B

(2)

To help Angela, her employer agrees to give her an interest free loan of $4000 to buy the car.

The employer is to recover the money by making the following deductions from Angela’s salary:

$x in the first month,

$y every subsequent month.

The total deductions after 20 months is $1540 and after 30 months it is $2140.

(d) Find x and y.

(4)

(e) How many months will it take for Angela to completely pay off the $4000 loan?

(2) (Total 15 marks)

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