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ACCA MA · Guided practice (Show me how)

Chapter 24: Interest

Interest - forwards to a future value, backwards to a present value

Money has a time cost, whether it is borrowed or tied up. Compounding carries a sum FORWARD by adding interest; discounting brings a future sum BACK by removing it. They are the same calculation in opposite directions.

Part (a) - forwards.

  1. A man invests $200 on 1 January each year. On 31 December each year simple interest is credited at 15%, but this interest is put in a separate account and does not itself earn interest. Find the total standing to his credit on 31 December following his FOURTH payment of $200.
  2. A man invests $500 now for 3 years with interest at 10% p.a., compounded. How much will be in his account after 3 years?
  3. A man invests $800 at 6% p.a. for 5 years. How much will be in his account at the end of 5 years?
  4. A credit card company charges a nominal rate of 2% per month. A customer has bought $100 of goods on credit. Calculate the amount owed after one year, and the annual percentage rate (APR).

Part (b) - backwards.

  1. What amount now is equivalent to $800 in 4 years time, with interest at 10% p.a.?
  2. What is the present value of $1,200 receivable in 12 years time, with interest at 13%? (Discount factor at 13% for year 12 = 0.231.)
  3. Interest is 12% p.a. What is the present value of $500 receivable in 1 years time and thereafter every year for a total of 8 receipts? (Annuity factor at 12% for years 1 to 8 = 4.968.)
  4. A man expects to receive $1,000 in each of 9 years, the first receipt being in 4 years time. What is the present value if interest is 8% p.a.? (Annuity factors at 8%: years 1 to 12 = 7.536; years 1 to 3 = 2.577.)
  5. Interest is 12% p.a. What is the present value of $5,000 receivable in 1 years time and thereafter in perpetuity?

Use the published three-decimal-place tables where a factor is quoted, and give money answers as the notes do.

  1. (a) Compounding forwards

    Calculate the four amounts in Part (a): the total standing to the credit of the man who invests $200 each year, on 31 December following his fourth payment; the balances after 3 years and after 5 years of the two compound investments; and the amount owed on the credit card after one year, with its annual percentage rate (APR).

  2. (b) Discounting backwards

    Calculate the present value of each amount in Part (b): $800 in 4 years' time, $1,200 in 12 years' time, $500 a year for 8 years, $1,000 a year for 9 years starting in 4 years' time (with the annuity factor for years 4 to 12), and $5,000 a year in perpetuity.

Opening this exercise…