a sum of rupees 10 is given as a loan to be returned in 6 monthly installment at rupees 2 what is the rate of interest
Answers
Step-by-step explanation:
Amount borrowed = Rs.10
Let rate of interest = R%
Simple Interest for Rs.10 for 6 months at R% = \begin{gathered}\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}\end{gathered}
100
10×R×
2
1
=
20
R
i.e, 10 +
20
R
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}
100
3×R×
12
4
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}
100
3×R×
12
1
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}(3+3+3+3+3+3)+
⎝
⎜
⎜
⎛
100
3×R×
12
5
+
100
3×R×
12
4
+...+
100
3×R×
12
1
⎠
⎟
⎟
⎞
= 10 +
20
R
18 + \dfrac{\dfrac{3\text{R}}{12}\left(5+4+...+1\right)}{100}=\text{ 10 + }\dfrac{\text{R}}{20}18+
100
12
3R
(5+4+...+1)
= 10 +
20
R
\begin{gathered}8 = \dfrac{\text{R}}{20} - \dfrac{15\text{R}}{400} = \dfrac{5\text{R}}{400}=\dfrac{\text{R}}{80}\\\\\text{R} = 640\%\end{gathered}
8=
20
R
−
400
15R
=
400
5R
=
80
R
R=640%