Below is a compilation of all the important compound and simple interest related formula for UPSC CSE Prelims' CSAT 2024 + 2025.

**Compound Interest** -- if 'r' is the rate % per annum, the amount 'P' for 1 year will be:

$$P\left({1 + {r \over 100}}\right)$$

That is, the *principle at the beginning of the year is to be multiplied by*:

$$\left({1 + {r \over 100}}\right)$$

Now, if 'n' be the number of complete years, then the amount 'P' after 'n' years will be:

$$Amount = P{\left({1 + {r \over 100}}\right)}^n$$

$$ \text{Compound Interest} = P{\left({1 + {r \over 100}}\right)}^n - P$$

$$Amount (A) = P + I$$

$$P = A - I$$

$$I = A-P$$

$$\text{Simple Interest, I} = \frac{P \times r \times t}{100} \text{[where, P = Principle, t = time, r = rate of interest]}$$

$$\text{P} = \frac{100 \times I}{t \times r}$$

$$\text{t} = \frac{100 \times I}{P \times r}$$

$$\text{r} = \frac{100 \times I}{P \times t}$$

- If the rate of intererst is uearly and interest is calculated
**half yearly**: divide the rate by 2 and multiply the time by 2 - If the rate of intererst is uearly and interest is calculated
**quarterly**: divide the rate by 4 amd multiply the time by 4 - If the rate of intererst is uearly and interest is calculated
**monthly**: divide the rate by 12 and multiply the time by 12

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