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# Important Formulas(Part 2) - Simple Interest

If a sum becomes $n$ times in T years at simple interest of R% per annum,

$\text{R}=\dfrac{100(\text{n}-1)}{\text{T}}$

Annual installment which will discharge a debt of D due in T years at simple interest of R% per annum

$=\dfrac{\text{100D}}{\text{100T}+\dfrac{\text{RT(T-1)}}{2}}$

Note: T must be an integer $\ge 1$

Monthly installment which will discharge a debt of D due in M months at simple interest of R% per annum

$=\dfrac{\text{100D}}{\text{100M}+\dfrac{\text{RM(M-1)}}{2×12}}$

Note: M must be an integer $\ge 1$

If an amount P1 is lent out at simple interest of R1% per annum and another amount P2 at simple interest of R2% per annum, then the rate of interest for the whole sum is R% where

$\text{R}=\dfrac{\text{P}_1\text{R}_1+ \text{P}_2\text{R}_2}{\text{P}_1+\text{P}_2}$

If a certain sum is lent out in $n$ parts at rates of R1%, R2%, ..., Rn% per annum for the time periods T1, T2, ..., Tn units, and equal simple interest is obtained on each part, then the ratio in which the sum is divided can be given by

$\dfrac{1}{\text{R}_1\text{T}_1}:\dfrac{1}{\text{R}_2\text{T}_2}:\cdots :\dfrac{1}{\text{R}_\text{n}\text{T}_\text{n}}$

If a certain sum P, lent out for a certain time T years, amounts to P1 at simple interest of R1% per annum and to P2 at simple interest of R2% per annum, then

$\text{P}=\dfrac{\text{P}_2\text{R}_1-\text{P}_1\text{R}_2}{\text{R}_1-\text{R}_2}\\\text{T}=\dfrac{\text{P}_1-\text{P}_2}{\text{P}_2\text{R}_1-\text{P}_1\text{R}_2}×100$