Question

A sum of rs. 10 is given as a loan to be returned in 6 monthly installments at rs.3. what is the rate of interest?

Answer 1

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Answer 2

Answer:

640%

Step-by-step explanation:

Amount borrowed = Rs.10

Let rate of interest = R%

Simple Interest for Rs.10 for 6 months at R% =  $\dfrac{10 \times \text{R} \times \dfrac{1}{2}}{100} = \dfrac{\text{R}}{20}\\\text{i.e, 10 + }\dfrac{\text{R}}{20}\text{ is due in 6 months}$

Payment after 1st month = Rs.3

Interest for this Rs.3 for the remaining 4 months = $\dfrac{3 \times R \times \dfrac{4}{12}}{100}$

Payment after 5th month = Rs.3

Interest for this Rs.3 for the remaining 1 month   = $\dfrac{3 \times R \times \dfrac{1}{12}}{100}$

Payment after 6th month = Rs.3 and this closes the loan

$(3 + 3 + 3 + 3 + 3 + 3) + \left(\dfrac{3 \times R \times \dfrac{5}{12}}{100} + \dfrac{3 \times R \times \dfrac{4}{12}}{100} + ... +\dfrac{3 \times R \times \dfrac{1}{12}}{100} \right) = \text{ 10 + }\dfrac{\text{R}}{20}$

$18 + \dfrac{\dfrac{3\text{R}}{12}\left(5+4+...+1\right)}{100}=\text{ 10 + }\dfrac{\text{R}}{20}$

$8 = \dfrac{\text{R}}{20} - \dfrac{15\text{R}}{400} = \dfrac{5\text{R}}{400}=\dfrac{\text{R}}{80}\\\\\text{R} = 640\%$

Hence the rate of interest is 640%