1.7 Amortization and annuitiesIB Maths: Applications and Interpretation SL: Subtopic test

1. 1
   Alicia takes out a loan of 12 000 USD to buy a car. Interest is charged at a nominal annual rate of 6%, compounded monthly. She repays the loan with equal payments at the end of each month for 4 years.

   (a)

   How many payments does Alicia make in total?

   [1 mark]

   • A4
   • B12
   • C48
   • D576

   (b)

   Use your GDC to find Alicia's monthly payment, to the nearest USD.

   [1 mark]

   • A282 USD
   • B250 USD
   • C60 USD
   • D1 527 USD

   (c)

   Calculate the total interest Alicia pays over the 4 years.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Ben deposits 200 EUR at the end of each month into an account that pays a nominal annual interest rate of 3.6%, compounded monthly. The account starts with a zero balance.

   (a)

   Use your GDC to find the balance of the account after 5 years.

   [1 mark]

   • A12 000.00 EUR
   • B13 126.32 EUR
   • C13 165.70 EUR
   • D14 321.22 EUR

   (b)

   How much interest does Ben earn in the 5 years?

   [1 mark]

   • A13 126.32 EUR
   • B12 000.00 EUR
   • C126.32 EUR
   • D1 126.32 EUR

   (c)

   Use your GDC to find the least number of months Ben must keep depositing so that the balance first exceeds 15 000 EUR.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A bank lends 150 000 AED to buy a flat. Interest is charged at a nominal annual rate of 4.5%, compounded monthly. The loan is repaid with equal payments at the end of each month over 20 years.

   (a)

   Use your GDC to find the monthly repayment.

   [3 marks]

   (b)

   (i) Find the total interest paid over the 20 years.
   (ii) Find the amount still owed immediately after the 60th payment.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Chen borrows 25 000 USD at a nominal annual interest rate of 7.2%, compounded monthly, and repays it with equal payments at the end of each month. He can afford to pay at most 520 USD per month.

   (a)

   (i) Use your GDC to find the least number of whole months in which Chen can repay the loan.
   (ii) Chen pays 520 USD for the first 56 months and a smaller final payment in month 57. Find the amount of the final payment.

   [6 marks]

   (b)

   Chen considers repaying the loan with equal monthly payments over exactly 5 years instead.
   (i) Find the monthly payment.
   (ii) Find the total interest he would pay.
   (iii) Compare this with the total interest in part (a), and state which plan costs Chen less in interest.

   [6 marks]

   Total for question 4: 12 marks

End of questions