Solve Problems Involving Compound Interest (10)

Connect the compound interest formula to repeated applications of simple interest using appropriate digital technologies (ACMNA229)

LO: To calculate compound interest.

Know:

  • What interest represents.

  • How to calculate simple interest.

  • What the main terms of interest represents, eg.) principle, time, rate and interest.

Understand:

  • That a quantity can grow by a set amount over a set period of time and that compound interest reinvests the interest amount gained at the end of each year for the following year.

Do:

  • I can calculate the compound interest gained of a quantity.

What is Interest?

Interest is something that occurs when people borrow money.

When people borrow money, it usually costs them something in order to borrow money.

What lenders charge is called interest.

Formula for Calculating Interest

I = PRT
I – Interest earned
P – Principle (amount starting/amount invested)
R- Rate (how much does it grow)
T – Time (length invested)

Compound Interest

Sometimes banks or lenders are sneaky, and what they do is charge you interest on top of the interest in order to make more money in the long run. This is called compound interest. This can also work in your favour if you invest your money wisely and invest the interest gained after every year.

It is basically earning “interest on interest“.

Compound interest is a repeated application of simple interest, where the interest earned at the end of each compound period is reinvested. 

Compound interest will produce a larger return on a long-term investment compared to simple interest.

Notice how interest is charged on top of the interest. So over the course of 5 years, the difference is $131.41.

Formula for Calculating Compound Interest

PV – is present value, basically what is the amount you currently owe or have invested.

r – is the interest rate, basically what percentage will they charge you per period. It’s usually written as a decimal number, so 5% is represented with 0.05.

n – is the number of periods (is it charged once per year – annually, or bi-annually – twice per year.)

FV – is the future value, what is the total amount you will owe or gain after all of the periods.

Formula for Calculating Compound Interest (Bi-annually/Quarterly/Monthly)

Sometimes there are situations where interest rates are charged or paid more than one time a year. The formula is similar but there are slight changes.

If it is charged bi-annually it means interest is charged every 6 months.

If it is charged quarterly it means interest is charged every 3 months.

If it is charged monthly it means that interest is charged 12 times a year.

If it is charged daily it means that interest is charged 365 times a year.

One common misconception is converting the rate of interest into rate percentage per period. For example, 5% p.a. compounded quarterly means it is 1.25% per period.

Interactives

Compound Interest Worksheets

compound-interest-worksheet-1.pdf
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compound-interest-worksheet-2.pdf
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compound-interest-worksheet-3.pdf
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compound-interest-worksheet-4.pdf
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compound-interest-worksheet-5.pdf
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Compound Interest Videos

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