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Welcome to our Math lesson on Compound Interest, this is the fifth lesson of our suite of math lessons covering the topic of Applications of Percentage in Banking. Simple and Compound Interest, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
Now that you know what a compound percentage change represents, it is much easier to understand the concept of compound interest and the corresponding interest rates applied in banking.
Compound interest, otherwise known as "interest on interest" occurs when a bank calculates the rates based on the actual deposit and not on the principal. In other words, compound interest (or compounding interest) is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. Compound interest is calculated together with the principal P (i.e. by calculating the total amount A) through the compound interest formula:
where n is the number of times the interest is compounded in a year (in our previous example n = 1, as the interest was compounded once in a year), r is the compound interest rate expressed as a decimal and t is the total period of deposit or loan. Then, the principal is subtracted from the amount A to give only the compound interest CI if required, i.e.
Let's get a better understanding of this through an example.
A customer deposits $3,600 in a bank that applies 1.2% compound interest rates every six months. Calculate:
We have the following clues:
P = $3,600
r = 1.2% = 0.012
n = 2 (every six months means twice a year)
t = 5
An = ?
CI = ?
You can also calculate other variables involved in the compound interest formula. For example, we can calculate the principal if the total amount after a certain period is given when the interest rate is known, etc. Let's consider another example.
A customer has $37,821 in his savings account. The bank offers an interest of 1.8% compounded thrice in a year. What was her balance four years ago?
The quantity to be calculated in this problem is the principal P. We have the following clues:
An = $37,821
r = 1.6% = 0.018
n = 3
t = 4
P = ?
Using the formula of compound interest
we obtain after substitutions
If we are asked to calculate the value of compound interest CI from this example, we can write
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