Interest and compounding

Banks advertise things like 'FD at 6% per annum' or 'savings account at 2.5% p.a.'. Interest is the extra money a bank pays you for keeping your money with them, and the extra you pay when you borrow. (A bit like lending a friend your bicycle and getting an ice cream every week in return.) p.a. means per annum: for every year.

In a Fixed Deposit (FD) you leave a set amount for a set time at a set rate. The money is locked until the end (maturity), and then you get your deposit back plus the interest.

Say you deposit ₹6000 at 10% p.a. The ₹6000 is the principal and 10% is the rate. After one year the interest is 0.10 × 6000 = ₹600, so you have 6000 + 600 = ₹6600. Put another way, the deposit becomes 110% of itself: 6000 × 1.1 = 6600.

Now leave it three years. There are two kinds of FD, and the difference matters.

Option 1, no compounding. The interest is paid out each year and the principal stays ₹6000. Every year you get ₹600, so after three years you've received ₹1800 of interest plus your ₹6000 back: ₹7800.

Option 2, with compounding. The interest is added back into the FD, so the principal grows:

Compounding wins: ₹7986 against ₹7800. As percentages of the deposit: 7800/6000 = 130%, a gain of 30%; 7986/6000 = 133.1%, a gain of 33.1%. The extra 3.1% is interest earned on interest.

In general, for principal p at rate r for t terms:

Values can fall the same way. A ₹21,000 TV losing (depreciating) 5% of its value a year is worth 0.95 × 21,000 = ₹19,950 after one year. A village of 1250 losing 10% a decade has 1250 × 0.9 × 0.9 × 0.9 ≈ 910 people after three decades. (Growing populations and bacteria work the same way, with the percentage taken on the newest total each time.)