How often Annuities, perpetuities and sinking funds is asked

Where it was asked

• May/Jun 201423.409999999999997 marks
• Oct/Nov 201329.96999999999999 marks
• May/Jun 201329.96999999999999 marks

The questions

1. May/Jun 2014, Q3multiple choice

   You want to save up R4 000 to buy a new phone. To do this, you deposit R100 into a savings account at the end of every month, and the account pays interest at 9% per annum, compounded monthly. Determine how long it will take to accumulate R4 000, giving your answer to the nearest month. Choose the correct option: [1] 18 months, [2] 35 months, [3] 48 months, [4] 494 months, [5] None of the above.

2. May/Jun 2014, Q8multiple choice

   A student has enrolled for a degree programme that runs for four years, and she has set aside a fund of R40 000 to help cover her expenses during this period. Assuming the fund earns interest at 7,5% per year compounded monthly, and she withdraws an equal amount at the beginning of each month over the four years, determine the size of each monthly withdrawal.

3. May/Jun 2014, Q12multiple choice

   Following a car accident caused by a faulty tyre, the Flat Tyre Company agreed to pay Kobelo, one of the drivers working for the Speedy Taxi services, an amount of R6 825 every month, forever (indefinitely). Given that money can earn 12,6% per year, compounded monthly, determine the lump sum that the Flat Tyre Company needs to have available right now in order to be able to fund all of these ongoing monthly payments to Kobelo.

4. May/Jun 2014, Q14multiple choice

   Thandi takes out an endowment policy with a maturity date 30 years from now. The interest rate she can expect to earn is 11,15% per year, compounded once a year. Her first yearly payment into the policy is R7 500, and thereafter each subsequent yearly payment increases by R800 more than the previous one. Determine the amount Thandi can expect to receive when the policy matures.

5. May/Jun 2014, Q20multiple choice

   Given the accumulated value formula S = R·s(with subscript n at rate i), express n in terms of the other variables. Which of the following expressions correctly denotes n?