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Level Four > Number and Algebra

Involving Interest

Purpose: 

This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

Achievement Objectives:

Achievement Objective: NA4-3: Find fractions, decimals, and percentages of amounts expressed as whole numbers, simple fractions, and decimals.
AO elaboration and other teaching resources

Specific Learning Outcomes: 

find percentage of whole numbers

Required Resource Materials: 
FIO, Link, Number, Book Three, Involving Interest, page 6
A classmate
A calculator
Activity: 

Kaylene reinvests the interest she earns back into her savings account, and so this activity introduces students to the concept of compounding interest, that is, interest paid on the interest. This has a surprisingly large effect on the investment, and Kaylene ends up with approximately 175% of her initial amount. Ensure that
the students understand how compounding interest works before they start this activity.
The students will need to have a system for keeping track of what is going on year by year. Using a table such as the one below is a good way of organising the information. You may like to discuss with the students how to round sensibly.

table.

Using a spreadsheet on a computer would also be a good way of organising the information. You could extend this activity by having the students develop a spreadsheet that will work out each end-of-year total automatically.
investigation
As well as using the concepts developed in the activity, the students will see in the investigation how interest rates vary depending on the length of the investment. You could discuss with them why this happens. Other useful discussion points for this page are:

• What is the effect of the frequency of interest payments? For example, will Kaylene earn more money in her investment if interest is paid monthly or yearly?

• What is the effect of compound interest on retirement savings, and why are people encouraged to start saving for their retirement early?

• What is the effect of compound interest on money borrowed? (Over a long period, such as a 25 year term, the interest paid will generally add up to more than the amount borrowed.)

Answers to Activity

1. Kaylene would get $1,771.56 from the Invercargill Investment Bank, $1,750.00 from the Titahi Bay Local Bank, and $1,760.91 from Martinborough Municipal Bank. (If you rounded these to the nearest whole dollar, the answers would be $1,772, $1,750, and $1,761 respectively.)
2. To get the most money back, Kaylene should bank her money with the Invercargill Investment Bank.
Investigation
Answers will vary.