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Money

3.0 Measurements · 3.3 Money

Syllabus tag: Kenya CBC | Grade 8 Mathematics | Strand 3.0 Measurements | Sub-Strand 3.3 Money (9 lessons)

Lesson objectives

By the end of this sub-strand, you should be able to:

  • Identify interest and principal, and calculate simple and compound interest
  • Work out appreciation and depreciation of value over time
  • Work out hire purchase in real-life situations
  • Spend money responsibly on needs and leisure

Money

Money borrowed costs more to repay than was taken. Money saved grows. A car loses value while a plot of land gains it. This topic puts numbers to all of that.

a) Principal and interest

The principal is the amount borrowed or invested at the start.

Interest is the extra amount paid for borrowing, or earned for saving.

The rate is the percentage charged each year, and the time is how long in years.

b) Simple interest

Simple interest is worked out on the original principal every year. It does not change.

Simple interest Simple interest interest = P × R × T / 100 the rule interest = 10000 × 10 × 2 / 100 KES 10 000 at 10% for 2 years interest = KES 2 000 the interest earned amount = 10000 + 2000 principal plus interest amount = KES 12 000 the total

The amount is the principal plus the interest, which is what you finally repay or withdraw.

Keep the time in years. Six months is 0.5 years, not 6.

c) Compound interest

Compound interest is added to the principal. The next year's interest is then worked out on a larger sum.

Compound interest Compound interest after year 1 = 10000 × 1.10 interest added on after year 1 = KES 11 000 this is the new principal after year 2 = 11000 × 1.10 interest on the larger amount after year 2 = KES 12 100 compare with 12 000

After two years, simple interest gives KES 12 000 and compound gives KES 12 100. The gap looks small here but grows quickly over more years.

A shortcut for compound: multiply by (1 + rate) once for each year.

d) Appreciation and depreciation

Appreciation is a rise in value over time. Land and buildings usually appreciate.

Depreciation is a fall in value. Vehicles, phones and machinery depreciate.

Depreciation works like compound interest in reverse. Multiply by (1 − rate) once for each year.

Take a car worth KES 500 000 depreciating at 15%. After one year it is worth 500 000 × 0.85 = KES 425 000. After two years, 425 000 × 0.85 = KES 361 250.

e) Hire purchase

Hire purchase buys goods by paying a deposit and then instalments. You use the item while paying.

Hire purchase Hire purchase deposit = KES 20 000 paid up front instalments = 12 × 5 000 one a month for a year instalments = KES 60 000 the total paid monthly total paid = 20000 + 60000 deposit plus instalments total paid = KES 80 000 cash price was 70 000

The hire purchase price is the deposit plus all the instalments.

It is always more than the cash price. Here it costs KES 10 000 extra, which is the price of paying later.

Hire purchase is not automatically a bad deal. It is a decision about whether spreading the cost is worth that extra.

f) Spending responsibly

A need is something you must have: food, school fees, medicine.

A want is something you would enjoy: a newer phone, an outing.

Meet needs first, then save, then spend on wants from what remains. Borrowing for a want means paying interest on something you could have done without.

g) Where this is used

A SACCO member compares loan rates. A shopkeeper decides whether to buy a fridge on hire purchase. A family budgets school fees against a monthly income.

Words to know

  • Principal -- the original amount of money borrowed, saved, or invested.
  • Simple interest -- interest calculated on the original principal only, the same amount each period.
  • Compound interest -- interest calculated on the growing balance, so interest earns further interest over time.
  • Hire purchase -- a method of paying for an item through a deposit followed by instalments.

:::checkpoint Check yourself

  1. Find the simple interest on KES 20 000 at 8% for 3 years.
  2. What is the amount after that time?
  3. A machine worth KES 100 000 depreciates at 20% a year. What is it worth after 2 years?
  4. Give one reason hire purchase costs more than paying cash. :::

Bridge to practice

Try the exercises below -- on simple and compound interest, appreciation, depreciation, and hire purchase.

Check yourselfPractise Money10 questions →Next in MathematicsDecimals