What is the difference between compound interest and simple interest on 2500 for 2 years at 4% per annum?

S.I = \(\frac{2500\times2\times4}{100}\) = Rs 200

C.I = 2500\(\big(1+\frac{4}{100}\big)^2\)- 2500 = 2500 x \(\frac{26}{25}\) x \(\frac{26}{25}\) - 2500

= 2704-2500 = Rs 204

C.I - S.I = Rs 204 - Rs 200 = Rs 4.

ML Aggarwal Solutions Class 9 Mathematics Solutions for Compound Interest Exercise 2.2 in Chapter 2 - Compound Interest

Question 7 Compound Interest Exercise 2.2

Find the difference between the simple interest and compound interest on 2 years at 4% per annum,

compound interest being reckoned semi-annually.

Answer:

It is given that

Principal (P) = ₹ 2500

Rate of interest (r) = 4% p.a. or 2% half-yearly

Period (n) = 2 years or 4 half-years

We know that

SI = Prt/100

Substituting the values

= (2500 × 4 × 2)/100

= ₹ 200

If compounded semi-annually

\begin{aligned} &\mathrm{A}=\mathrm{P}(1+\mathrm{r} / 100)^{\mathrm{n}}\\ &\text { Substituting the values }\\ &=2500(1+2 / 100)^{4} \end{aligned}

By further calculation

= 2500 × 51/50 × 51/50 × 51/50 × 51/50

= ₹ 2706.08

We know that

CI = A – P

Substituting the values

= 2706.08 – 2500

= ₹ 206.08

So the difference between CI and SI = 206.08 – 200 = ₹ 6.08

Was This helpful?

P = ₹ 2,500
r = 4% p.a. = `(4)/(2)` = 2% half yearly
T = 2 year = 4 half years

A = P`(1 + r/100)^n`

= ₹ 2,500 `(1 + 2/100)^4`

= ₹ 2,500 `(1 + 1/50)^4`

= ₹ 2,500 `((51)/(50))^4`

= ₹`(2,500 xx 51 xx 51 xx 51 xx 51)/(50 xx 50 xx 50 xx 50)`

= ₹ `(51 xx 51 xx 51 xx 51)/(50 xx 50)`

= ₹ `(2,601 xx 2,601)/(2,500)`

= ₹`(67,65,201)/(2,500)`

= ₹ 2,706·08
C.I. = A - P

= ₹ (2,706·08 - ₹ 2,500)
= ₹ 206·08
and S.I. = `"PRT"/(100) = ₹ (2,500 xx 4 xx 2)/(100)` = ₹ 200

Difference between C.I. and S.I.
= C.I. - S.I.
= ₹ 206·08 - ₹ 200
= ₹ 6·08.

Find the difference between CI & SI or 2 years at 12% rate of interest. If principal is Rs. 2500. 

1. Rs. 24
2. Rs. 36
3. Rs. 32
4. Rs. 28

Answer (Detailed Solution Below)

Option 2 : Rs. 36

Free

15 Questions 15 Marks 8 Mins

Given: 

The principal = Rs. 2500

Rate of interest = 12%

Time = 2 years

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

⇒ (2500 × 12 × 2)/100

⇒ 25 × 12 × 2

⇒ Rs. 600 

Now, Compound interest for 2 years is 

⇒ 2500[(1 + 12/100)2 – 1]

⇒ 2500[(112/100)2 – 1]

⇒ 2500 × (28/25)2 – 2500

⇒ 2500 × (784/625) – 2500

⇒ 3136 – 2500

⇒ Rs. 636

Now, The difference between CI and SI is

⇒ Rs. 636 – Rs. 600

⇒ Rs. 36

∴ The difference between CI and SI is Rs. 36. 

Alternate Method

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

The  difference is 

⇒ 2500(12/100)2

⇒ 2500 × 144/10000

⇒ Rs. 36

∴ The difference between CI and SI is Rs. 36. 

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