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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?

## 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.