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# KS3 Science & Maths - Breaking News!: Econometrics

## Stimulus Questions

Econometrics are mathematical and statistical techniques trying to explain patterns in growth and recession in the economy!

• How is econometrics used to test economic theories?

• What kinds of graphs might be used in econometrics?

## GCSE Bitesize - Data Handling and Business Studies ## MM50: Interest Rates

Simple Interest

Simple interest is calculated only on the principal amount, or on that portion of the principal amount that remains unpaid.

The amount of simple interest is calculated according to the following formula: $I_{simp} = r \cdot B_0 \cdot m$

where r is the period interest rate (I/m), B0 the initial balance and m the number of time periods elapsed.

To calculate the period interest rate r, one divides the interest rate I by the number of periods m.

For example, imagine that a credit card holder has an outstanding balance of $2500 and that the simple interest rate is 12.99% per annum. The interest added at the end of 3 months would be, $I_{simp} = \bigg( \frac{0.1299}{12} \cdot 2500 \bigg) \cdot 3 = 81.19$ and they would have to pay$2581.19 to pay off the balance at this point.

Compound Interest

A formula for calculating annual compound interest is $A = P \left(1 + \frac{r}{n}\right)^{nt}$

Where,

• A = final amount
• P = principal amount (initial investment)
• r = annual nominal interest rate (as a decimal, not in percentage)
• n = number of times the interest is compounded per year
• t = number of years

Example usage: An amount of 1500.00 is deposited in a bank paying an annual interest rate of 4.3%, compounded quarterly. Find the balance after 6 years.

A. Using the formula above, with P = 1500, r = 4.3/100 = 0.043, n = 4, and t = 6: $A=1500\left(1 + \frac{0.043}{4}\right)^{4 \times 6} =1938.84$

So, the balance after 6 years is approximately 1,938.84.

## Math is fun Have a go at finding some more information using the search engines in the boxes below.  Sweet Search and ipl2 both look for useful information for students on the internet.

Here are some ideas of keywords to search for: ## Sweet Search - a search engine for students

Try to find out more using Sweet Search, a search engine designed to help students find reliable information.

## Kids.net.au - Encyclopedia ## KS3 Bitesize - Representing Data 