Frequency of compounding

Two deposits can both advertise the same annual rate and still pay different amounts. The difference comes down to how often interest is actually added to the balance.

The frequency of compounding is that count — how many times a year interest gets calculated and credited. Once a year is annual compounding. Four times a year is quarterly. Twelve times a year is monthly.

The more often interest is added, the sooner it starts earning interest of its own. So a higher frequency of compounding always produces a higher actual return, even when the stated annual rate is identical.

When the compounding frequency changes, two numbers move together: the rate used for each period, and the number of periods. An investment paying 8% a year, compounded quarterly, earns 8% divided by 4, or 2% per quarter, over 4 periods a year rather than 1.

The workbook is explicit that a higher frequency of compounding means interest is paid on interest more often, so returns earned through compounding are higher. This is distinct from the future value formula itself — the frequency of compounding is the adjustment that has to be made correctly before that formula can be used.

Rs 5,00,000 invested for 5 years at 8% p.a., compounded annually, grows to Rs 7,34,664 — total interest of Rs 2,34,664.

The same Rs 5,00,000, at the same 8% p.a., compounded quarterly instead — 2% for 20 quarters rather than 8% for 5 years — grows to Rs 7,42,974, or Rs 8,310 more, for no extra rupee invested and no extra day of waiting. The only change was how often the interest was added back in.

Chapter 2 (Time Value of Money), section 2.2.2, explains the frequency-of-compounding adjustment as part of building up to the future value formula. Expect a question that gives an annual rate and a compounding frequency and asks for the correctly adjusted rate and period count, or a conceptual question on why quarterly compounding beats annual compounding at the same stated rate.

• Adjust the rate and the number of periods together — 8% compounded quarterly is 2% for 20 periods over 5 years, never 8% for 20 periods.
• A higher frequency of compounding never lowers the return. If a calculation shows the opposite, the rate was divided but the period count was not multiplied to match.
• Do not confuse compounding frequency with how often an annuity pays out — one is about how often interest is calculated inside a single investment, the other is about how often money is paid out to an investor.