On what sum of money will the difference between the simple interest and compound interest for 3 years?

On what sum of money will the difference between the compound interest and simple interest for 2 years be equal to Rs. 25 if the rate of interest charged for both is 5% p.a.?

Solution

C.I = `P[(1 + r/100)^2 - 1] = P[(1 + 5/100)^2 - 1] = "41P"/400`

`S.I = (P xx 5 xx 2)/100 = P/100`

Given, C.I. - S.I. Rs. 25

`=> "41P"/400 - P/10 = 25`

`=> (41P - 40P)/400 = 25`

`=> P = 10000`

∴ Required sum  = Rs. 10,000

Concept: Concept of Compound Interest - Compound Interest as a Repeated Simple Interest Computation with a Growing Principal

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Question

On what sum of money will the difference between the compound interest and simple interest for 2years be equal to Rs 25 if the rate of interest charged for both is 5% p.a. 

Hint:

Use the formula of compound interest and simple interest to get the principal amount.

The correct answer is: Rs 10000

Complete step by step solution:Let the principal amount = PIt is given that the rate of interest R = 5% and number of years T = 2 years.So, compound interest for 2 years = Simple  interest for 2 years = It is given that compound interest - simple interest = 25 RupeesThat is,  Rupees.Hence the principal amount = Rs 10000

On what sum of money will the difference between simple interest and compound interest for 2 years at 5% per annum be equal to Rs. 63/-

1. Rs. 24600/-
2. Rs. 24800/-
3. Rs. 25200/-
4. Rs. 25500/-

Answer (Detailed Solution Below)

Option 3 : Rs. 25200/-

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Given: 

Time is 2 years

Rate is 5% per annum

The difference between simple interest and compound interest is Rs. 63.

Concept: 

S.I = (P × R × T)/100

C.I = P[(1 + r/100)n - 1]

Here, n is the number of terms in the year

Calculation: 

Let sum be Rs. P 

Now, 

The simple interest for 2 years at 5% per annum is

(P × 5 × 2)/100

⇒ P/10 

Now, 

The compound interest for 2 years at 5% per annum is

P[(1 + 5/100)2 - 1]

⇒ P[(21/20)2 - 1]

⇒ P[(441/400) - 1]

⇒ 41P/400 

So, 

The difference between Compound interest and simple interest is 

⇒ 41p/400 - P/10 = 63

⇒ 41P - 40P = 63 × 400

⇒ P = Rs. 25200 

∴ The required sum of money is Rs. 25200.

The difference between compound interest and simple interest for 2 years is 

⇒ P(r/100)2

According to question 

⇒ P(5/100)2 = 63

⇒ P × 1/400 = 63

⇒ P = 63 × 400 

⇒ P = 25200 

∴ The required sum of money is Rs. 25200

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