Practice Questions for Simple & Compound Interest | CRE 3

1. CRE 3 - Simple & Compound Interest | Simple & Compound Interest

The difference between S.I. and C.I. on a certain sum of money at 5% p.a. for 2 years is Rs. 30. Find the sum.

(a)
Rs. 11,200
(b)
Rs. 11,800
(c)
Rs. 12,000
(d)
Rs. 12,400

Answer: Option C

Explanation :

CI for 2 years = $[P {(1 + \frac{5}{100})}^{2} - P]$

SI for 2 years = $\frac{P \times 5 \times 2}{100}$

Difference = $[P {(1 + \frac{5}{100})}^{2} - P] - \frac{P \times 5 \times 2}{100} = 30$

= $(1 . 05^{2} P - P) - 0.1 P = 30$

⇒ (1.1025P – P) – 0.1P = 30

⇒ 0.0025P = 30

⇒ P = 12000

Hence, option (c).

2. CRE 3 - Simple & Compound Interest | Simple & Compound Interest

I invested Rs. 30,000 at S.I. for 2 years @ 12% p.a. How much more or less would have been my return, if I had invested it at C.I. @ 11% p.a.

(a)
Loss Rs. 237
(b)
Loss Rs. 362.8
(c)
Gain Rs. 300
(d)
Gain Rs.321.2

Answer: Option A

Explanation :

S.I. = $\frac{30000 \times 2 \times 12}{100} = 7200$

C.I. = $30000 \{{(1 + \frac{11}{100})}^{2} - 1\} = 6963$

∴ Loss = 7200 – 6963 = Rs. 237.

Hence, option (a).

3. CRE 3 - Simple & Compound Interest | Simple & Compound Interest

A man borrowed Rs. 8000 for $2 \frac{1}{2}$ years at 14% p.a. simple interest and lent the whole amount for the same time and at the same rate C.I. How much did he gain?

(a)
Rs. 320.4
(b)
Rs. 351
(c)
Rs. 324.58
(d)
Rs. 342.54

Answer: Option C

Explanation :

S.I. = $\frac{8000 \times 5 \times 14}{100 \times 2} = 2800$

C.I = $8000 \{{(1 + \frac{14}{100})}^{2} \times (1 + \frac{\frac{14}{2}}{100}) - 1\} = 3124.576$

∴ gain = 3124.576 – 2800 = 324.58

Hence, option (c).

4. CRE 3 - Simple & Compound Interest | Simple & Compound Interest

The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is:

(a)
625
(b)
630
(c)
640
(d)
650

Answer: Option A

Explanation :

Let the sum be Rs. x. Then,

C.I. = $[x {(1 + \frac{4}{100})}^{2} - x] = (\frac{676}{625} x - x) = \frac{51}{625} x$

S.I. = $\frac{x \times 4 \times 2}{100} = \frac{2 x}{25}$

$\Rightarrow \frac{51 x}{625} - \frac{2 x}{25} = 1$

∴ x = 625.

Hence, option (a).

5. CRE 3 - Simple & Compound Interest | Simple & Compound Interest

If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same at the same rate and for the same time?

(a)
Rs. 51.25
(b)
Rs. 52
(c)
Rs. 54.25
(d)
Rs. 60

Answer: Option A

Explanation :

Sum = Rs. $\frac{50 \times 100}{2 \times 5} =$ Rs. 500

Amount = Rs. $[500 \times {(1 + \frac{5}{100})}^{2}]$

C.I. = Rs. (551.25 - 500) = Rs. 51.25

Hence, option (a).

6. CRE 3 - Simple & Compound Interest | Simple & Compound Interest

The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?

(a)
8
(b)
10
(c)
12
(d)
Cannot be determined
(e)
None of these

Answer: Option A

Explanation :

$[15000 \times {(1 + \frac{R}{100})}^{2} - 15000] - (\frac{15000 \times R \times 2}{100}) = 96 \Rightarrow 15000 [{(1 + \frac{R}{100})}^{2} - 1 - \frac{2 R}{100}] = 96 \Rightarrow 15000 [\frac{{(100 + R)}^{2} - 10000 - (200 \times R)}{10000}] = 96 \Rightarrow R^{2} = \frac{96 \times 2}{3} = 64$

⇒ R = 8.

∴ Rate = 8%.

Hence, option (a).

7. CRE 3 - Simple & Compound Interest | Simple & Compound Interest

The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?

(a)
8
(b)
10
(c)
12
(d)
Cannot be determined
(e)
None of these

Answer: Option A

Explanation :

$[15000 \times {(1 + \frac{R}{100})}^{2} - 15000] - (\frac{15000 \times R \times 2}{100}) = 96 \Rightarrow 15000 [{(1 + \frac{R}{100})}^{2} - 1 - \frac{2 R}{100}] = 96 \Rightarrow 15000 [\frac{{(100 + R)}^{2} - 10000 - (200 \times R)}{10000}] = 96 \Rightarrow R^{2} = \frac{96 \times 2}{3} = 64$

⇒ R = 8.

∴ Rate = 8%.

Hence, option (a).

8. CRE 3 - Simple & Compound Interest | Simple & Compound Interest

The difference between simple interest and compound on Rs. 1200 for one year at 10% per annum reckoned half-yearly is:

(a)
Rs. 2.50
(b)
Rs. 3
(c)
Rs. 3.75
(d)
Rs. 4
(e)
none of these

Answer: Option B

Explanation :

S.I. = Rs. $\frac{1200 \times 10 \times 1}{100} =$ Rs. 120

C.I. = $[1200 \times {(1 + \frac{5}{100})}^{2} - 1200] =$ Rs. 123

∴ Difference = Rs. (123 - 120) = Rs. 3.

Hence, option (b).

CRE 3 - Simple & Compound Interest | Simple & Compound Interest

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