Find the sum on which the difference between the simple interest and the compound interest at the rate of 8% per annum compounded annually be ₹64 in 2 years.
Tell the answer by taking sum as ₹100.
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Find the sum on which the difference between the simple interest and the compound interest at the rate of 8% per annum compounded annually be ₹64 in 2 years.
Tell the answer by taking sum as ₹100.
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Correct Question
Find the sum on which the difference between the simple interest and the compound interest at the rate of 8% per annum compounded annually be ₹64 in 2 years.
Answer
Given :
Difference : ₹64
Rate of interest : 8%
Time : 2 years
To find :
The sum invested at the bank.
Solution :
First, we'll find the simple interest.
Simple interest :
[tex]\sf \dashrightarrow SI = \dfrac{P \times R \times T}{100}[/tex]
[tex]\sf \dashrightarrow \dfrac{P \times 8 \times 2}{100}[/tex]
[tex]\sf \dashrightarrow \dfrac{P \times 16}{100}[/tex]
[tex]\sf \dashrightarrow \dfrac{16P}{100} = \dfrac{4P}{25}[/tex]
Now, let's find the compound interest.
Compound interest :
[tex]\sf \dashrightarrow Amount = Principle \bigg( 1 + \dfrac{Rate}{100} \bigg)^{Time}[/tex]
[tex]\sf \dashrightarrow P \bigg( 1 + \dfrac{8}{100} \bigg)^{2}[/tex]
[tex]\sf \dashrightarrow P \bigg( 1 + \dfrac{2}{25} \bigg)^{2}[/tex]
[tex]\sf \dashrightarrow P \bigg( \dfrac{25 + 2}{25} \bigg)^{2}[/tex]
[tex]\sf \dashrightarrow P \bigg( \dfrac{27}{25} \bigg)^{2}[/tex]
[tex]\sf \dashrightarrow P \bigg( \dfrac{729}{625}[/tex]
[tex]\sf \dashrightarrow \dfrac{729P}{625}[/tex]
Now, let's find the principle value.
Principle (sum) :
[tex]\sf \dashrightarrow Difference = CI - SI[/tex]
[tex]\sf \dashrightarrow 64 = \dfrac{729P}{625} - \dfrac{4P}{25}[/tex]
[tex]\sf \dashrightarrow 64 = \dfrac{729P - 100P}{625}[/tex]
[tex]\sf \dashrightarrow 64 = \dfrac{639P}{625}[/tex]
[tex]\sf \dashrightarrow 639P = 64(625)[/tex]
[tex]\sf \dashrightarrow 639P = 40000[/tex]
[tex]\sf \dashrightarrow P = \dfrac{40000}{639}[/tex]
[tex]\sf \dashrightarrow P = 62.59[/tex]
Hence, the principle (sum) amount is ₹62.59.