Find the compound interest on Rs 1000 for two years at the rate of 3 compounded half yearly

Directions: Read the followin questions carefully and answer them:

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• Question No. 1
• Correct Option: B
• Question No. 2
• Correct Option: A
• Question No. 3
• Correct Option: C
• Question No. 4
• Correct Option: B
• Question No. 5
• Correct Option: D
• Question No. 6
• Correct Option: C
• Question No. 7
• Correct Option: A
• Question No. 8
• Correct Option: D
• Question No. 9
• Correct Option: A
• Question No. 10
• Correct Option: D

1

Find compound interest on Rs. 7000 at 21% per annum for 2 years 4 months, compounded annually.

A. Rs. 3824.9

B. Rs. 3966.1

C. Rs. 4094.4

D. Rs. 11109

2

Find the compound interest on Rs. 7500 in 2 years at 6% per annum, the interest being compounded half-yearly.

A. Rs. 941.31

B. Rs. 834.44

C. Rs.746.21

D. Rs. 764

3 Find the compound interest on Rs. 10,000 at 20% per annum for 6 months. compounded quarterly.

A. Rs.4353

B. Rs. 1329

C. Rs. 1025

D. Rs. 2649

4

If the simple interest on a sum of money at 5% per annum for 2 years is Rs. 1400, find the compound interest on the same sum for the same period at the same rate.

A. Rs. 1023

B. Rs. 1435

C. Rs. 3232

D. Rs. 1255

5

If Rs. 1000 amounts to Rs. 1166.40 in two years compounded annually, Find the rate of interest per annum.

A. 2% p.a

B. 4% p.a

C. 6% p.a

D. 8% p.a

6

If the compound interest on certain sum at 16	2	%  for 3 years is Rs. 1270. Find the simple interest on
3

the same sum at the same rate for the same period .

A. Rs. 1202

B. Rs. 1104

C. Rs. 1080

D. Rs. 1432

7

The difference between the compound interest and simple interest on certain sum at 10% per annum for 2 years is Rs. 175. Find the sum .

A. Rs. 17500

B. Rs. 17854

C. Rs. 17533

D. Rs. 17132

8

The difference between the compound interest and simple  interest accrued on an amount of Rs. 18,000 in 2 years was Rs. 720. What was the Rate of interest p.c.p.a.?

A. 5%

B. 10%

C. 15%

D. 20%

9

Divide Rs. 841 between A and B, so that the amount of A after 7 years is equal to the amount of B after 9 years, the interest being compounded at 5% per annum.

A. Rs. 441 and  Rs. 400

B. Rs. 453 and Rs. 564

C. Rs. 321 and Rs. 583

D. Rs. 349 and Rs. 867

10

A certain sum amounts to Rs. 6250 in 2 years and to Rs. 6875 in 3 years. Find the sum.

A. Rs. 5674.69

B. Rs. 4233

C. Rs. 5254.45

D. Rs. 5165.29

Question No. 1

Correct Option: B

Explanation:

Time = 2 years 4 months = 2	4	years  = 2	1	years.
12	3

Let principal = P, Rate = R% per annum, Time = n years.

When interest is compounded annually. then,

Amount  =  P	(	1 +	R	)	n
100

So, amount = Rs	[	7000 ×	(	1 +	21	)	2	]	×	(	1 +	1/3 × 21	)]
100		100

⇒  Rs.	(	7000 ×	121	×	121	×	107	)
100	100	100

⇒  10966.1.

So, C.I. = Rs. (10966.1 – 7000)  ⇒  Rs. 3966.1.

Hence, option B is correct.

Question No. 2

Correct Option: A

Explanation:

When interest is compounded Half-yearly. then,

Amount = P	[	1 +	(R/2)	]	2T
100

Principal  = Rs. 7500; Rate = 3% per half - year; Time = 2 years = 4 half - years.

So, Amount = Rs.	[	7500 ×	(	1 +	3	)	4	]
100

⇒   Rs.	(	7500  ×	103	×	103	×	103	×	103	)
100	100	100	100

⇒  Rs. 8441.31

⇒ C.I = Rs. (8441.31 - 7500)  = Rs. 941.31.

Hence, option A is correct.

Question No. 3

Correct Option: C

Explanation:

P = 10000, T = 6 months, R = 20/4 = 5%   (rate of interest apply quaterly)

By the net% effect we would calculate the effective compound rate of interest for 6 months = 10.25%  (Refer to sub-details)

CI = 10.25% of 10000

CI =	10.25 × 10000	= 1025.
100

_________________________________________________________________

Sub-details:

Calculation of effective compound rate of interest for 2 quaters (6 months) will be as follows.

Here, x = 5 and y = 5%

Net% effect = x + y =	xy
100

= 5 + 5 +	5 × 5	= 10 + 0.25 = 10.25%
100

_______________________________________________________

Traditional Method:

When interest is compounded Quarterly. then,

Amount = P	[	1 +	(R/4)	]	4T
100

Principal = Rs. 10000; Time = 6 months = 2 quarters; Rate = 20% per annum = 5% per quarter

So, Amount = Rs	[	10000 ×	(	1 +	5	)	2	]
100

⇒  Rs	(	10000 ×	21	×	21	)	⇒ 11025.
20	20

So, C.I = Rs (11025 – 10000) ⇒  Rs 1025.

Hence, option C is correct.

Question No. 4

Correct Option: B

Explanation:

We know, that

SI = rt%  (rate of interest & time)  and  by the net% effect we would calculate the effective compound rate of interest for 2 years = 10.25% (Refer to sub-details)

1400 = (2 × 5)%

So, 10% ≡ ₹ 1400

10.25% ≡ ₹ x

By the cross multiplication, we get

x =	1400 × 10.25	= ₹ 1435.
10

_______________________________________________________________________

Sub-details:

Calculation of effective compound rate of interest for 2 years will be as follows.

Here, x = 5 and y = 5%

Net% effect = x + y =	xy
100

= 5 + 5 +	5 × 5	= 10 + .25 = 10.25%
100

_______________________________________________________________________

Traditional Method:

Clearly, Rate = 5% p.a, Time = 2 years, S.I = Rs. 1400.

So, principal = Rs.	(	100 × 1400	)	= Rs. 14000.
2 × 5

Amount = Rs.	[	14000 ×	(	1 +	5	)	2	]	⇔ Rs.	(	14000 ×	21	×	21	)	⇒ Rs. 15435.
100		20	20

So, C.I = Rs. (15435 – 14000) = Rs. 1435.

Hence, option B is correct.

Question No. 5

Correct Option: D

Explanation:

Principal = Rs. 500; Amount = Rs. 583.20; Time = 2 years.
Let the rate be R% per annum. then,

[	1000	(	1 +	R	)	2	]	= 1166.40.
100

                   

Or

(	1 +	R	)	2	=	(	108	)	2
100		100

⇒ 1 +	R	=	108	or  R = 8.
100	100

So, Rate = 8% p.a

Hence, option D is corret.

Question No. 6

Correct Option: C

Explanation:

Let the sum be Rs. x, then,

C.I =	[	x  ×	(	1 +	50	)	3	– x	]	=	(	343x	– x	)	=	127x	.
3 × 100		216	216

So,	127x	= 1270 or x =	1270 × 216	= 2160.
216	127

 

Thus, the sum is Rs. 2160.

So, S.I = Rs	(	2160 ×	50	× 3 ×	1	)	= Rs 1080.
3	100

Hence, option C is correct.

Question No. 7

Correct Option: A

Explanation:

Method I:

To solve this question, we can apply a short trick approach

Sum =	Difference × 1002
r2

Given,

Difference = 175,  r = 10%

By the short trick approach, we get

Sum =	175 × 1002	= 17500/-
102

_____________________________________________________

Method II:

We can solve it by the net% formula,

Rate % of SI for 2 yr at 10% pa = 10 × 2 = 20%

Rate % of CI for 2 yr at 10% pa,

= 10 + 10 +	10 × 10	= 21%
100

% rate difference of CI and SI = 21% – 20 = 1%

Let the sum be x, then

1% of x = 175

x =	175 × 100	= ₹ 17500
1

Hence, option A is correct.

Question No. 8

Correct Option: D

Explanation:

To solve this question, we can apply a short trick approach

Sum =	Difference × 1002
r2

Given,

Sum (Amount) = 18000,  Difference = 720,  r = ?

By the short trick approach, we get

18000 =	720 × 1002	⇒ r2 =	720 × 1002	⇒ r2 = 400   ⇒   r = 20%
r2	18000

Hence, option D is correct.

Question No. 9

Correct Option: A

Explanation:

Let the two parts be Rs. x and Rs. (841 – x).

x	(	1 +	5	)	7	= (841 – x)	(	1 +	5	)	9
100		100

⇒	x	=	(	1 +	5	)	2	=	(	21	×	21	)	.
(841 – x)	100		20	20

⇒ 400x = 441 (841 – x)  ⇒ 841x = 441 × 841   ⇒   x = 441.

So, the two parts are Rs. 441 and Rs. (841 – 441) i.e Rs. 441 and Rs. 400.

Hence, option A is correct.

Question No. 10

Correct Option: D

Explanation:

SI for 1 year = Rs.(6875 – 6250) = Rs. 625.

So, Rate =	(	100 x 625	)	% = 10%.
6250 × 1

Let the sum be Rs. x, then,

x	(	1 +	10	)	2	= 6250   ⇔  x ×	11	×	11	= 6250.
100		10	10

⇒   x =	(	6250 ×	100	)	= 5165.29.
121

So, Sum = Rs. 5165.29.

Hence, option D is correct.