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
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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.
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.
Find the difference between CI & SI or 2 years at 12% rate of interest. If principal is Rs. 2500.
- Rs. 24
- Rs. 36
- Rs. 32
- 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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