Compounding

The idea

In compounding, the interest gained each term is added back to the principal, so the principal and the interest both increase every term and the final amount is more than without compounding.

Two ways to keep ₹6000 for 3 years

A bank offers an FD of ₹6000 at 10% p.a. for 3 years. Option 1: the interest is paid out to you every year. Option 2: the interest is added back to the FD every year.

After 3 years, which option gives more money?

• Option 1: interest paid out
• Option 2: interest added back
• Both give the same

Year by year, two ways

The top bar pays the interest out, so every year adds the same block. The bottom bar adds the interest back, so the principal grows and so does each block. Move through the years and answer the goal.

Interest that earns interest

In compounding, the interest gained each term is added back to the principal, so the principal and the interest both increase every term, and the final amount is more than without compounding.

₹6000 at 10%, interest added back: Year 1: 6000 + 600 = ₹6600 Year 2: 6600 + 660 = ₹7260 Year 3: 7260 + 726 = ₹7986

Each year the interest is 10% of a bigger principal: 600, then 660, then 726.

Without compounding, the 3 years gave ₹7800. With compounding they give ₹7986, which is ₹186 more, because the interest earned interest too.

Notes

In compounding, the interest gained each term is added back to the principal, so the principal and the interest both increase every term, and the final amount is more than without compounding.

Check yourself

₹5000 is put in an FD at 10% p.a. and the interest is added back every year. How much is in the account after 2 years (in ₹)?

Answer: 6050

Year 1: 5000 + 500 = ₹5500 Year 2: 5500 + 550 = ₹6050

For the same FD (₹5000, 10% p.a., interest added back), how much interest is earned in the 2nd year (in ₹)?

Answer: 550

The principal for year 2 is ₹5500. 0.10 × 5500 = ₹550

What happens to the principal when the interest is compounded?

₹1000 is kept for 2 years at 10% p.a. How many rupees more does compounding give than paying the interest out (in ₹)?

Answer: 10

With compounding: 1000 → 1100 → 1210 Paid out: 1000 + 100 + 100 = 1200 Difference: 1210 − 1200 = ₹10

• The interest of each year is added to it, so it grows — correct. Yes! The next year's interest is then worked out on the bigger principal.
• It stays the same every year. That is without compounding, where the interest is paid out. With compounding the interest is added back.
• It is paid out to you every year. It is the interest that is added back, not paid out. The principal grows with it.