Find the difference between the C.I and S.I. on rs 500 at 10 p.a. for 2 years

Find the difference between the compound interest and simple interest. On a sum of Rs 50,000 at 10% per annum for 2 years.

Given: 
P = Rs 50, 000
R = 10 % p. a.
n = 2 years
We know that amount A at the end of n years at the rate R % per annum when the interest is
compounded annually is given by A = P\[\left( 1 + \frac{R}{100} \right) . \]
\[ \therefore\text{ A = Rs }50, 000 \left( 1 + \frac{10}{100} \right)^2 \]
\[ =\text{ Rs }50, 000 \left( 1 . 1 \right)^2 \]
 = Rs 60, 500
Also,
CI = A - P
 = Rs 60, 500 - Rs 50, 000
= Rs 10, 500
We know that: 
\[SI = \frac{PRT}{100}\]
\[ = \frac{50, 000 \times 10 \times 2}{100}\]
= Rs 10, 000
∴ Difference between CI and SI = Rs 10, 500 - Rs 10, 000
= Rs 500

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Solution

Step 1: Determine the simple and compound interest.Assume that the principle amount is P.So, the simple interest is:SI=P×R×T100⇒S I=P×10×2100∴SI=0.2PSimilarly, the compound interest is:CI=P(1+R100)T-P⇒ CI=P1+101002-P⇒CI=1.21P-P∴CI=0.21P So, the simple and compound interests are 0.2Pand0.21P respectively.Step 2: Determine the amount.The difference in the interests is Rs.500.The equation for the difference of interests is:0.21P-0.2P=Rs.500⇒0.01P=Rs.500⇒ P=Rs. 50000The sum after the interest is compounded annually is A=P1+101002.Determine the amount: (adsbygoogle = window.adsbygoogle || []).push({}); A=P1+101002⇒A=Rs.50000×1.21 ∴A=Rs.60500So, the sum is Rs.60500

The difference between the compound interest and simple interest on a certain sum of money at 10% per annum for 2 years is Rs 500. Find the sum when the Interest is compounded annually.

1. Rs 50000
2. Rs 55000
3. Rs 40000
4. Rs 65000

Answer (Detailed Solution Below)

Option 1 : Rs 50000

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Given

The difference between the compound interest and simple interest on a certain sum of money at 10% per annum for 2 years is Rs 500.

Formula used

CI - SI = (P × R2)/(100)2

CI = Compound interest

SI = Simple interest

P = Principal

R = Rate

Calculation

According to question

⇒ 500 = (P × (10)2)/10000

⇒ P = (500 × 10000)/100

∴ Principal is Rs.50000

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Find the difference between CI & SI for 2 years at 8% rate of interest. If the principal is 625 rupee.

1. 2
2. 4
3. 8
4. 6

Answer (Detailed Solution Below)

Option 2 : 4

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Given: 

The principal is 625 rupee

Rate is 8%

Concept: 

SI = (P × R × T)/100

CI = P[(1 + r/100)n - 1]

Here, n is the number of terms in the year.

Calculation: 

The simple interest for 2 years

⇒ (625 × 8 × 2)/100

⇒ 25 × 2 × 2

⇒ 100 rupee

Now, Compound interest for 2 years is 

⇒ 625[(1 + 8/100)2 - 1]

⇒ 625[(108/100)2 - 1]

⇒ 625[(108)2 - (100)2] × 1/10000

⇒ (208 × 8)/16

⇒ 104 rupee

Now, The difference between CI and SI is

⇒ 104 - 100

⇒ 4

∴ The difference between CI and SI is 4. 

The difference between CI and SI for 2 years is P(r/100)2

The  difference is 

⇒ 625(8/100)2

⇒ 625 × 4/625

⇒ 4

∴ The difference between CI and SI is 4. 

This short trick works only for 2 years.

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