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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Case I :
Here P1 = Rs.5000 and r = 6%
So, Amount after 1 year
= `"P"(1 + "r"/100)`
= `5000(1 + 6/100)`
= `5000 xx (106)/(100)`
= 5300
Amount after 2 year
= `"P"(1 + "r"/100)`
= `5300(1 + 6/100)`
= `5300 xx (106)/(100)`
= 5618
Thus, P3 = Rs.5618 and r = 6%
Amount after 3 year
= `"P"(1 + "r"/100)`
= `5618(1+ 6/100)`
= `5618 xx (106)/(100)`
= 5955.08
Hence,
Amount = Rs.5955.08
Also, C.I.
= A - P
= Rs.5955.08 - Rs.5000
= Rs. 955.08
Case II :
Simple interest = `(5000 xx 6 xx 3)/(100)`
= 900
Difference between C.I. and S.I.
= Rs.955.08 - Rs.900
= Rs.55.08.
The difference between compound interest and simple interest at the same rate on Rs. 5000 for 2 years is Rs. 72. Find the rate of interest per annum.
- 12%
- 14%
- 16%
- 18%
Answer (Detailed Solution Below)
Option 1 : 12%
Free
10 Questions 10 Marks 7 Mins
Given:
Difference between Compound Interest (CI) and Simple Interest (SI) = Rs. 72
Principal (P)= Rs. 5000
Time (t) = 2 years
Formula used:
Difference between CI and SI for 2 years = PR2/1002
Where R is the Rate of Interest.
Calculation:
Using the above formula:
72 = (5000 × R2)/1002
⇒ R2 = 720/5 = 144
⇒ R = 12%
∴ The rate of interest is 12%
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The difference between simple and compound interest for a sum of Rs. 5,000 lent at 12% per annum in 2 years is
- Rs. 720
- Rs. 12
- Rs. 72
- Rs. 700
Answer (Detailed Solution Below)
Option 3 : Rs. 72
Free
20 Questions 30 Marks 18 Mins
Given:
The sum = Rs. 5000
The time = 2 years
The rate = 12%
Formula used:
The difference between CI and SI for two years = \(P \times {({R\over 100})^2}\) Where, P = Principle, and R = Rate
Calculation:
Let the difference between CI and SI be X
⇒ X = \(5000 \times {({12\over 100})^2}\) = \({5000\ \times {144\over 10000}}\ =\ {5\ \times 14.4}\ =\ Rs.\ 72\)
∴ The required result will be Rs. 72.
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