Solving Problems About Saving – Simple Interest and Problems Involving Saving (Primary 6 Mathematics) | Ganzaa

Simple Interest and Problems Involving Saving

Lessons

Primary 6 · Mathematics

Simple Interest and Problems Involving Saving

5 lessons

Lesson 5 of 5

Solving Problems About Saving

15 min

Let's begin

Ishimwe's P6 class wants to visit Akagera National Park at the end of the year. The trip will cost 90 000 Frw for the whole class. The class leader asks, "If we all save a little every week, how long will it take?" Saving problems like this mix everything you have learned in this unit.

A plan for money problems

Write down what you know: P, R, T, I, A, or the money in and out.
Decide what the question wants.
Choose the right rule and calculate step by step.
Check that the answer makes sense.

Worked example 1: regular saving

30 pupils each save 300 Frw a week.
Class savings each week = 30 × 300 = 9 000 Frw.
Weeks needed = 90 000 ÷ 9 000 = 10 weeks.

Worked example 2: saving with interest

Keza deposits 60 000 Frw in a SACCO at 6% simple interest per year for 3 years.
I = 60 000 × 6 × 3 ÷ 100 = 10 800 Frw.
A = 60 000 + 10 800 = 70 800 Frw.

Worked example 3: which offer is better?

Gatete has 100 000 Frw to save. Bank A pays 5% per year for 4 years. SACCO B pays 7% per year for 3 years.
Bank A: I = 100 000 × 5 × 4 ÷ 100 = 20 000 Frw.
SACCO B: I = 100 000 × 7 × 3 ÷ 100 = 21 000 Frw.
SACCO B pays 1 000 Frw more, and Gatete gets his money a year sooner. A higher rate alone does not prove an offer is better; you must also look at the time.

Worked example 4: shopping and saving

Mama Uwase has 50 000 Frw. She buys 3 kg of meat at 5 000 Frw per kg, 10 kg of rice at 1 200 Frw per kg and 2 L of cooking oil at 3 000 Frw per litre. (These are example prices.)
Meat: 3 × 5 000 = 15 000 Frw. Rice: 10 × 1 200 = 12 000 Frw. Oil: 2 × 3 000 = 6 000 Frw.
Total spent = 15 000 + 12 000 + 6 000 = 33 000 Frw.
Money saved = 50 000 − 33 000 = 17 000 Frw.

Worked example 5: is a loan worth it?

Gatete borrows 200 000 Frw at 12% per year for 1 year to buy a sewing machine. With it he makes 25 000 Frw profit each month.
He must repay A = 200 000 + 24 000 = 224 000 Frw.
In a year he makes 25 000 × 12 = 300 000 Frw.
After repaying, he has 300 000 − 224 000 = 76 000 Frw, and he owns the machine. The loan was a good decision.

Tip

Before you calculate, ask: "Does the question want the interest, or the whole amount?" Many marks are lost by stopping at the interest.

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Try it yourself

25 pupils each save 400 Frw a week. How many weeks until they have 50 000 Frw?
40 000 Frw is saved at 5% simple interest per year for 3 years. Find the amount.
Which gives more interest on 50 000 Frw: 6% per year for 2 years, or 4% per year for 3 years?
Keza gets 5 000 Frw pocket money a month and spends 3 200 Frw. How much does she save in 6 months?

Answers

25 × 400 = 10 000 Frw a week, and 50 000 ÷ 10 000 = 5 weeks.
I = 6 000 Frw, so A = 46 000 Frw.
Both give 6 000 Frw interest, so they are equally good.
She saves 1 800 Frw a month, and 1 800 × 6 = 10 800 Frw.

Quick check

20 pupils each save 500 Frw a week. How many weeks until the class has 60 000 Frw?

What you learned today

List what you know, then choose the right rule.
To compare offers, work out the interest of each one; do not look at the rate alone.
Check whether the question wants the interest or the total amount.

Sources and credits

Mathematics Grade 8, 1.7 Working with money: Budgets, savings, discount, interest and exchange rates, by Siyavula and volunteers, provided by Siyavula, licensed under CC BY 3.0. Adapted by Ganzaa.
The saving problems in this lesson. Written by Ganzaa.

1A plan for money problems