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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 P_{1} is lent out at simple interest of R_{1}% per annum and another amount P_{2} at simple interest of R_{2}% 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 R_{1}%, R_{2}%, ..., R_{n}% per annum for the time periods T_{1}, T_{2}, ..., T_{n} 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 P_{1} at simple interest of R_{1}% per annum and to P_{2} at simple interest of R_{2}% per annum, then

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

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