Question

Calculate the difference between the compound interest and the simple interest on Rs.10,000at 5p.c.p.a for

2 years.​

Answer 1

Answer:

Simple interest(SI)= Rs.1000

Compound interest(CI)= Rs. 1025

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Answer 2

Given :

• Principal = Rs. 10000
• Rate = 5%
• Time = 2 years

To find :

• difference between the compound interest and the simple interest

Solution :

$\sf{Amount = P \times \Bigg\lgroup 1 + \bigg(\dfrac{r}{100} \bigg)^{2} \Bigg\rgroup }$

             $\sf{ = 10000 \times \Bigg\lgroup 1 + \bigg(\dfrac{5}{100} \bigg)^{2} \Bigg\rgroup }$

             $\sf{ = 10000 \times \Bigg\lgroup 1 + \bigg(\dfrac{1}{20} \bigg)^{2} \Bigg\rgroup }$

              $\sf{ = 10000 \times \Bigg\lgroup 1 + \bigg(\dfrac{1}{20} \bigg)^{2} \Bigg\rgroup } [L.C.M \: of \: 20 \: is \: 1 \: and \: 20]$

              $\sf{ = 10000 \times \Bigg\lgroup 1 + \bigg(\dfrac{(1 \times 20) + (1 \times 1) }{20} \bigg)^{2} \Bigg\rgroup }$

              $\sf{ = 10000 \times \bigg(\dfrac{ 20 + 1 }{20} \bigg)^{2} \Bigg$

              $\sf{ = 10000 \times \bigg(\dfrac{ 21 }{20} \times \dfrac{ 21 }{20} \bigg) \Bigg$

              $\sf{ = 10000 \times \bigg(\dfrac{441 }{400 } \bigg) \Bigg$

              $\sf{ = 100 \not0 \not 0 \times \bigg(\dfrac{441 }{4 \not 0 \not0 } \bigg) \Bigg$

              $\sf{ = 100 \times \bigg(\dfrac{441 }{4 } \bigg) \Bigg$

              $\sf{ = \dfrac{44100}{4 }$

              = 11025

Compound Interest = Amount - Principal

                                 = 11025 - 10,000

                                 = 1025

Therefore, Compound Interest is Rs. 1025.

Simple Interest = $\sf \dfrac{p \times r \times t }{100}$

                         = $\sf \dfrac{10000 \times 5 \times 2 }{100}$

                         = $\dfrac{100000}{100}$

                         = 1000

Therefore, Simple Interest is Rs. 1000.

Differcene = Compound Interest - Simple Interest

                  = 1025 - 1000

                  = 25

Therefore, difference is Rs. 1025.