Compounding period
The interval, such as monthly, quarterly or annually, over which interest is calculated and added to an investment — the more often it happens within a year, the faster the investment grows.
In plain language
An interest rate quoted 'per annum' does not always mean interest is actually paid once a year. It might be paid every month, every quarter, or every year — and each of these is a different compounding period.
The shorter the compounding period, the more often interest gets added to the balance, and the sooner that added interest starts earning interest of its own. Two deposits that quote the same annual rate can end up worth different amounts, purely because one compounds more often than the other.
How it works
The workbook's own comparison: the Post Office Monthly Income Scheme (MIS) pays interest every month, while the Senior Citizens Scheme pays every quarter. The greater the frequency of compounding, the greater the return, because interest is paid on interest more often.
When the compounding period is shorter than a year, both the rate and the period count in the future value formula must be adjusted: the annual rate is divided by the number of compounding periods in a year, and the number of years is multiplied by that same number. An 8% annual rate compounded quarterly becomes 2% per period, run over 4 times n periods, not 8% run over n periods.
The formula
FV = PV x (1 + r/m)^(n x m)
m = number of compounding periods per year
r = annual (nominal) rate
n = number of years
A worked example
Krishna invests Rs 5,00,000 for 5 years at an 8% annual rate.
Compounded annually (m = 1):
FV = 5,00,000 x (1.08)^5 = Rs 7,34,664
Compounded quarterly (m = 4, so 2% for 20 periods):
FV = 5,00,000 x (1.02)^20 = Rs 7,42,974
The quarterly compounding period earns Rs 8,310 more than annual compounding, on the exact same rate and the exact same money, simply because interest is paid — and starts earning interest of its own — four times as often.
Why NISM asks about it
Chapter 2, section 2.2.2 (Future value), works the Krishna example across annual and quarterly compounding periods to show why frequency matters. Expect a question that hands you an annual rate and a compounding frequency other than annual, and expects you to adjust both the rate and the number of periods before applying the formula.
Common exam traps
- The single most common error: adjusting the rate for the compounding period but forgetting to adjust the number of periods to match, or vice versa. Both must move together.
- A shorter compounding period always raises the future value on the same nominal rate — if your answer goes the other way, check your period count.
- Simple interest has no compounding period at all, because the interest is paid out, not reinvested — see future value for the distinction.
Check yourself
1.If an investment pays 8 per cent per annum compounded quarterly, the applicable rate for each compounding period is:
- a)8 per cent
- b)4 per cent
- c)2 per cent
- d)0.67 per cent
Show the answer
Answer: (c) 2 per cent
"If an investment pays 8% interest p.a. compounded QUARTERLY, then the applicable rate of return for each compounding period is 8%/4, or 2%." Note that the number of periods must also be adjusted: over 5 years there are 20 quarterly periods, not 5.
2.The formula for future value is:
- a)FV = PV / (1 + r)^n
- b)FV = PV x (1 + r)^n
- c)FV = PV x r x n
- d)FV = PV + (PV x r)
Show the answer
Answer: (b) FV = PV x (1 + r)^n
FV = PV x (1 + r)^n, where r is the rate of return for each compounding period and n is the number of compounding periods. FV = PV / (1 + r)^n is the present value formula rearranged, and PV x r x n would give simple interest rather than a compounded future value.
Where this is taught
Free preparation for NISM Series X-ARelated terms
- Annuity tableA pre-computed table that gives the present-value multiple, or annuity factor, for a given interest rate and number of years, letting you value a regular cash flow without solving the formula each time.
- Compound interest rateThe rate at which a present sum of money grows into the future once its interest is reinvested and starts earning interest of its own, the forward-looking twin of the discount rate.
- Future valueWhat a sum of money invested today will be worth at a future date once returns have been earned and reinvested — the compounding half of the time value of money.
- Discount rateThe rate used to bring a future cash flow back to today's value — the higher this rate, the lower a given future amount is worth in present-day rupees.