7.4. Compound Interest

You might have come across statements like “one year interest for FD (fixed deposit) in the bank @ 9% per annum” or ‘Savings account with interest @ 5% per annum’. Interest is the extra money paid by institutions like banks or post offices on money deposited (kept) with them. Interest is also paid by people when they borrow money.

Interest is essentially the reward you receive for allowing a bank to use your money or the cost you incur when borrowing money. For example, if you deposit ₹1000 in a bank for one year at an interest rate of 5%, you will earn ₹50 as interest by the end of the year. Conversely, if you borrow ₹1000 from a bank at a similar rate, you will also have to pay ₹50 in interest by the end of the year.

Think of it as lending money to a friend. If they promise to return your ₹100 after a week along with ₹5 as appreciation for borrowing, that ₹5 is the interest.

We already know how to calculate Simple Interest. Example 7: A sum of ₹10,000 is borrowed at a rate of interest 15% per annum for 2 years. Find the simple interest on this sum and the amount to be paid at the end of 2 years.

Simple Interest is calculated on the original principal amount during the entire period of the loan. In our example, the interest for one year on ₹10,000 at 15% would be 15% of ₹100, or ₹1,500. Therefore, for 2 years, it would be ₹1,500 x 2 = ₹3,000. The total amount to be repaid after 2 years would then be the principal plus the interest, which totals ₹10,000 + ₹3,000 = ₹13,000.

Imagine you lent your friend ₹10,000 and agreed they would pay you back ₹1,500 every year for 2 years. The total they owe you after 2 years would be similar to the example above.

Normaly, the interest paid or charged is never simple. The interest is calculated on the amount of the previous year. This is known as interest compounded or Compound Interest (C.I.).

Compound interest differs because it calculates interest on both the initial principal and the accumulated interest from previous periods. For example, if you invest ₹20,000 at 8% compounded annually, the first year would yield ₹1,600 (as simple interest), leading to a new total of ₹21,600. In the second year, the interest is then calculated on ₹21,600, which results in a higher interest amount for the second year.

Consider planting a tree that grows taller each year. The height of the tree after the first year was a certain amount, and this amount contributes to how much it grows in the second year. The growth builds upon itself like how interest compounds.

Calculating Compound Interest: A sum of ₹20,000 is borrowed by Heena for 2 years at an interest of 8% compounded annually. Find the Compound Interest (C.I.) and the amount she has to pay at the end of 2 years.

To find the compound interest, we first calculate the interest for the first year: ₹20,000 at 8% gives us ₹1,600. This means at the end of the first year, Heena would have ₹21,600. For the second year, we calculate 8% of ₹21,600, which is ₹1,728. By adding up the interest from both years, Heena's total interest would be ₹1,600 + ₹1,728 = ₹3,328. Ultimately, the total amount due at the end of 2 years would be ₹20,000 + ₹3,328 = ₹23,328.

It's like a feedback loop of growth – every year, you not only earn on your initial investment but also on what you previously earned, creating an ever-increasing return.

Note that in 3 years, Interest earned by Simple Interest = ₹30, whereas, Interest earned by Compound Interest = ₹33.10.

This illustrates the primary difference between simple and compound interest. After 3 years, you can see that the compound interest yields more income compared to simple interest because it continually builds on the previous amount’s interest. It's crucial to appreciate this difference because it can significantly affect financial returns over a long period.

Imagine saving ₹100 in a piggy bank that gathers interest. If it's a simple interest piggy bank, it adds a fixed amount each year. If it's a compound interest piggy bank, every year's interest adds more to the base amount for future interest calculations.

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