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IB Mathematics: Applications and Interpretation SL · 12.2: Finance · 12.2.2

Name Date

Amortisation and annuities Problem set B

Use the Finance Solver. Write down every box. N counts payments.

Each question matches the question with the same number in set A. Do the ones you got wrong there.

Difficulty: first skills applying them stretch

Skills

  1. A loan of €15 000 charges 4.2% per year, compounded monthly, and is repaid monthly over 4 years. Find (a) the monthly payment, (b) the total repaid, (c) the total interest.

  2. Dev can afford to repay £520 a month for 15 years. A bank charges 4.6% per year, compounded monthly. Find the largest loan Dev can take.

  3. $220 is saved at the end of every month in an account paying 3.3% per year, compounded monthly. Find the amount after 6 years.

  4. €250 000 is paid into a fund earning 3.5% per year, compounded yearly. Equal amounts are taken out at the end of each year for 25 years, emptying the fund. Find each amount.

  5. A student wants to have £12 000 in 5 years' time to buy a car. She pays an equal amount into an account at the end of each month. The account pays 3.6% per year, compounded monthly. (a) How much must she pay in each month? (b) How much of the £12 000 is interest?

In context

  1. Pedro borrows £7500 at 7.2% per year, compounded monthly, and repays £200 a month. How many payments does he make?

  2. A fund holds £90 000 and earns 3.0% per year, compounded monthly. £1100 is taken out at the end of each month. For how many months does the money last?

  3. Ines borrows €6500 to buy a laptop and a desk. Plan 1 charges 8.4% per year, compounded monthly, over 2 years. Plan 2 charges 7.8% per year, compounded monthly, over 3 years. Both are repaid with equal payments at the end of each month. For each plan find (a) the monthly payment and (b) the total repaid. (c) Which plan costs less overall, and by how much?

Stretch

  1. A house loan of $240 000 charges 3.9% per year, compounded monthly, and is repaid monthly over 20 years. (a) Find the monthly payment. (b) Find the amount still owed after 8 years.

jmaths.xyz · AI SL · 12.2.2 Amortisation and annuities