Compound interest rate
The 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.
In plain language
Money invested today does not just sit still — it earns a return, and if that return is left in the investment, it starts earning a return of its own. The rate used to project this growth into the future is the compound interest rate.
It is the same rate that appears in reverse as the discount rate, which brings a future amount back to what it is worth today. The workbook treats them as two directions along the same road: the compound interest rate moves money forward in time, the discount rate moves it backward.
How it works
When present inflows are increased at a relevant rate to reach their future values, that rate is called the compound interest rate. It compounds because interest is calculated not only on the original amount but on the interest already earned and left invested.
The workbook's own worked contrast: Rs 1,000 received after 3 years, discounted at 5%, is worth Rs 864 today; the same Rs 1,000 discounted at 8% is worth only Rs 794 today. Run the same numbers forward instead, and 5% or 8% becomes the compound interest rate that grows today's money into that future Rs 1,000. The higher the rate, the faster money grows forward and the less a future rupee is worth today — the two effects move together.
The formula
FV = PV x (1 + r)^n
r = compound interest rate (per compounding period)
The same r, used the other way, is the discount rate: PV = FV / (1 + r)^n
A worked example
Geeta invests Rs 2,00,000 in a fixed deposit at a compound interest rate of 7% per annum, compounded annually, for 5 years.
FV = 2,00,000 x (1.07)^5 = Rs 2,80,510
Her money grows by Rs 80,510 over 5 years because the 7% is compounded — interest earned in year 1 goes on to earn interest in years 2 through 5. Had she instead withdrawn the interest each year and spent it, her return would have been simple interest of Rs 14,000 a year, or Rs 70,000 in total, Rs 10,510 less.
Why NISM asks about it
Chapter 2, section 2.1, defines the compound interest rate as one of the named rates — alongside the discount rate and the reinvestment rate — the reader must recognise before working any time-value problem. Expect a question that asks you to identify which rate is being used in a given scenario, forward-looking (compound interest) or backward-looking (discount).
Common exam traps
- 'Compound interest rate', 'discount rate', 'rate of return' and 'reinvestment rate' are, per the workbook, all names for the same underlying rate, used in different directions of a calculation — do not treat them as different numbers.
- Compounding is not the same as a higher stated rate. A lower rate compounded more frequently can still out-earn a higher rate paid as simple interest, once interest is left to earn interest.
- Always check whether the rate given is annual or per compounding period before using it — see compounding period.
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.
- Compounding periodThe 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.
- 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.