Finding an Unknown Rate, Tenure or Instalment in FD/RD

Both the FD formula and the RD formula relate several quantities to one another, so given any set of them except one, the missing quantity can be found by rearranging the formula.

In a Fixed Deposit, given $A$, $t$ and the compounding frequency, the rate $r$ can be found by isolating $\left(1+\dfrac{r}{100n}\right)^{nt} = \dfrac{A}{P}$ and recognising the right-hand side as a power that matches a whole-number rate — exactly the recognition method already used in Class 11's Compound Interest chapter (no logarithms are needed at this syllabus's scope, since the numbers in every problem here are chosen so the power is a recognisable perfect power).

In a Recurring Deposit, the maturity-value formula

can be rearranged for whichever quantity is unknown:

• Unknown instalment $P$: since both terms on the right contain $P$, factor it out — $M = P\left[n + \dfrac{r\,n(n+1)}{2400}\right]$ — and divide $M$ by the bracketed expression.
• Unknown rate $r$: rearrange directly, $r = \dfrac{2400(M-Pn)}{Pn(n+1)}$. …