Simple vs Compound Interest: Worked in Rupees Over 30 Years

Simple interest is paid only on the amount you started with. Compound interest is paid on the amount you started with *plus* the interest already added to it. Over a year or two the difference is small enough to ignore. Over twenty it is not. Here is the same deposit worked through both ways, then the loan-side version of the same idea, where a "flat" rate hides what a loan really costs.

One deposit, worked both ways

Take ₹1,00,000 at 7% a year. Simple interest adds ₹7,000 every year: P × r × t. Compound interest adds 7% of the current balance, which grows each year: P × (1 + r/n)^(n × t), where n is the number of times a year interest is added.

After one year, simple and yearly compounding are identical: there has been no interest yet to earn interest. After five years compounding is ahead by ₹5,255, after twenty by ₹1,46,968, and after thirty the compounded balance is almost two and a half times the simple one. The gap grows faster every year because each year's interest is calculated on a larger balance.

How often interest is added

Compounding more often helps, but by less than the table's layout might suggest. The fair way to compare is the effective annual rate: what the balance actually grows by in a year.

• 7% compounded quarterly: (1 + 0.07/4)^4 − 1 = 7.19% a year.
• 7% compounded monthly: (1 + 0.07/12)^12 − 1 = 7.23% a year.

Over 30 years monthly compounding ends ₹50,424 ahead of yearly, which is real money but small next to the ₹4,51,226 that compounding at all adds over simple interest. When comparing two deposits, compare the effective rates, not the headline rates: 7.15% compounded yearly earns less than 7% compounded quarterly, which is 7.19% effective. The headline rate alone doesn't say how often a deposit compounds, so check the bank's terms.

Where simple interest still shows up

• Interest you take out. A deposit that pays its interest into your savings account each quarter, instead of adding it to the deposit, grows with simple interest: the principal never changes.
• "Flat" loan rates. This is the one that costs money.

The flat-rate loan trap

Some lenders quote a flat interest rate: interest on the full original amount for the whole term, even though you repay part of the principal every month. Take ₹1,00,000 over 3 years at a 10% flat rate:

• Interest: ₹1,00,000 × 10% × 3 = ₹30,000.
• EMI: (₹1,00,000 + ₹30,000) ÷ 36 = ₹3,611.11.

The same loan at 10% on a reducing balance (the way a normal EMI works, where each month's interest is charged only on what you still owe) has an EMI of ₹3,226.72 and total interest of ₹16,161.87. To make a reducing-balance loan cost ₹3,611.11 a month, the rate has to be 17.92%. So a 10% flat rate costs as much as 17.92% on a reducing balance: nearly double, because you pay interest on money you have already paid back. When a loan is quoted as flat, ask for the reducing-balance rate (the APR) before comparing it with anything else, or check it yourself: the EMI Calculator with ₹1,00,000, 36 months and 17.92% shows ₹3,611.23, within 12 paise of the flat-rate EMI (the exact equivalent is 17.918%).

A quick mental check

The Rule of 72 estimates how long money takes to double under compounding: divide 72 by the rate. At 7%, 72 ÷ 7 = 10.3 years; the exact answer is 10.24 years. It works for yearly compounding at everyday rates and drifts for very high ones.

Running your own numbers

For a single deposit, the two formulas above are all you need: P × r × t for simple interest and P × (1 + r/n)^(n × t) for compound. For regular monthly investing rather than one lump sum, the Investment Compound Interest Calculator adds contributions. It works in US dollars, but the arithmetic is the same in rupees, and with the monthly contribution set to 0 it compounds a single deposit yearly, quarterly or monthly.