The last time, I did a presentation on what simple interest is and how to calculate it. You can check the post here. In the article, I will explain what compound interest is and how to calculate it and the other components involved in compound interest.
Compound interest is a little different from Simple interest, but they do share the same components such as Principal, Amount and other components I have explained in the Simple Interest article. Now one major difference between simple interest and compound interest is the Principal. In Simple interest, the Principal remains unchanged. The interest at every given period is also constant too. But that is not so in compound interest.
In compound interest, the interest is added to the Principal at the end of each circle or time. As a result, the Principal increases or compounds each time the interest pays out. The new Principal becomes greater than the original one. The interest continues to be added to Principal each period interest is paid. As a result, the next principal and interest generated increases at the beginning of the next circle.
The difference of amount between the initial amount at the end of a particular period and the one for the next period is called compound interest. This interest is continually added to the next Principal, hence it is called compound Interest. Now we are going to look at how to calculate Compound interest and other compounds that is connected with it.
First of all, we will use the manual method of finding the interest each year, adding it to the principal and finally determining the Compound interest.
Here are two examples:
Example 1: Calculate the compound interest on a loan of $4600 for 4 years at a rate of 5% per annum.
Solution
Year 1: 5% of Capital added to the capital
= (5/100)x4600
= 0.05x4600
= 230 + Capital
= 230 + 4600
= 4,830
Year 2: 5% of the new Capital.
= (5/100)x4830
= 0.05x4830
= 241.5 + Capital
= 241.5 + 4830
= 5,071.5
Year 3: 5% of the new Capital
= (5/100)x5071.5
= 0.05x5071.5
= 253.6 + Capital
= 5325.1
Year 4: 5% of the new Capital
= (5/100)x5325.1
= 0.05x5325.1
= 266.3 + Capital
= 266.3+5325.1
= 5,591.4
To get the compound interest finally, we need to find the difference between the original amount and the final amount.
Compound interest = 5,591.4 - 4600 = $991.4
Example 2: Calculate the compound interest on $200 for 3 years at 8% per annum.
Solution:
Year 1: 8% of the capital added to the capital
= (8/100)x200
= 0.08x200
= 16 + capital
= 16 + 200
= 216.
Year 2: 8% of the capital added to the capital
= (8/100)x216
= 0.08X216
= 17.28 + capital
= 17.28 + 216
= 233.28
Year 3: 8% of the capital added to the capital
= (8/100)x233.28
= 0.08x233.28
= 18.66 + capital
= 18.66 + 233.38
= 252.04
The compound interest is the difference between the original amount and the final amount.
Compound Interest = 252.04 - 200 = $52.04
This is a long way to calculate compound interest by manually adding the interest to the capital. It may be suitable for a few years calculation. However, when calculating for several years, this will surely take time. So in our next presentation, we will be able to derive a formula for calculating compound interest no matter how long the time involved is. But for few years calculations, the above manual method will suffice.
