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6.10

## National STEM Learning Centre

Skip to 0 minutes and 8 secondsMICHAEL ANDERSON: So let's take a look at simple interest. Now, simple interest is where you invest amounts, and you get a fixed percentage back at the end of each year. So for example, we could invest 500 pounds, with a simple interest of 3% that's paid at the end of the year. So how much money would we get back on that investment?

Skip to 0 minutes and 25 secondsPAULA KELLY: OK, so simply interest, the amount of interest we get stays the same. We've got 500 pounds. And we're going to invest that with a simple interest rate of 3%. So again, lots of ways of working up, set to different amounts. If we used our multiply method to our 3%-- say, parts 100, divided by 100. If we times it by 500 pounds, it will get us 3% off our 500 pounds. That's going to give us 15 pounds of interest. Every single year, we have that money in the bank, we'll get 15 pounds of interest.

Skip to 1 minute and 3 secondsMICHAEL ANDERSON: OK, so the 500 stays the same. Then every year, we'll get paid 15 pounds.

Skip to 1 minute and 7 secondsPAULA KELLY: Perfect. OK, so we'll give you one to have a go at home. If we invested 800 pounds for five years, and let's have the simple interest rate at 4%.

Skip to 1 minute and 27 secondsSo try this yourselves. Pause the video. And then press play again and see if you're right.

Skip to 1 minute and 36 secondsMICHAEL ANDERSON: OK, so how much would we get in the first year?

Skip to 1 minute and 41 secondsPAULA KELLY: OK, so using our decimal multiplier again, we've got 4% now. So add 100. You've got 0.04. It's off our 800 pounds.

Skip to 1 minute and 53 secondsSo again, we'd use a calculator. That's going to give us, every single year, 32 pounds. So every year, we have that money in the bank, that's our interest. We've said here we're going to invest for five years. So we've got five lots of our 32 pounds. So 150 and 10, we're going to have 160 pounds of interest. So we still got 800 pounds in the bank. It earned 160 pounds in interest.

# Simple interest

Probably one of the most common places we see percentages being used is with interest rates. Interest rates for savings accounts indicate the amount the bank pays you for every year you keep your money in a savings account. Interest rates for loans indicate the amount you must pay back each year in addition to the loan.

There are two types of interest: simple interest and compound interest.

Simple interest is used to calculate returns on certain kinds of investments. As its name suggest, it is relatively easy to calculate. The interest is calculated as a percentage of the initial amount invested (or borrowed) over a fixed period of time. There are three pieces of information we need:

• The initial (principle) sum invested.
• The interest rate usually expressed as an annual percentage rate.
• The length of time of the investment.

## Example one

I invest £500 at an annual interest rate of 2% per year and I invest for a period of 5 years.

Each year the investment earns 2% of £500. 2% of £500 is £10. As I invested for 5 years, at the end of the five years I receive an interest payment of £50.

## Example two

I invest £4000 at an annual interest rate of 10% but I withdraw my investment after 3 months. How much interest am I owed?

The interest owed after one year would be 10% of £4000, which would be £400.

However, I only invested for three twelfths of a year so I only receive $$\frac{3}{12}$$ of £400.

I would receive £100 interest payment.

In the video Paula and Michael go through some more examples. Have a go at this question before watching the second example:

I invest £800 at an annual interest rate of 4% and have my investment for 5 years. How much interest will I earn at the end of 5 years?

## Problem worksheet

Complete questions 14 and 15 from this week’s worksheet.