Compound Interest Questions

FACTS  AND  FORMULAE  FOR  COMPOUND  INTEREST  QUESTIONS

 

 

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

I.

1.  When interest is compound Annually:

Amount =P1+R100n

2.  When interest is compounded Half-yearly:

Amount = P1+(R2)1002n

3.  When interest is compounded Quarterly:

Amount = P1+R41004n

 

II.

1.  When interest is compounded Annually but time is in fraction, say 325 years.

Amount = P1+R1003×1+25R100

2.  When Rates are different for different years, say R1%, R2%, R3% for 1st, 2nd and 3rd year respectively.

Then, Amount = P1+R11001+R21001+R3100

 

III.  Present worth of Rs. x due n years hence is given by:

Present Worth = x1+R100n

Q:

The compound interest on rs.30000 at 7% per annum is Rs.4347. The period is

A) 2 years B) 2.5 years
C) 3 years D) 4 years
 
Answer & Explanation Answer: A) 2 years

Explanation:

Amount = Rs.(30000+4347) = Rs.34347

 

let the time be n years

 

Then,30000(1+7/100)^n = 34347

 

(107/100)^n = 34347/30000 = 11449/10000 = (107/100)^2

 

n = 2years

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416 103316
Q:

A sum of money amounts to Rs.6690 after 3 years and to Rs.10,035 after 6 years on compound interest.find the sum.

A) 4360 B) 4460
C) 4560 D) 4660
 
Answer & Explanation Answer: B) 4460

Explanation:

Let the sum be Rs.P.then
P(1+R/100)^3=6690…(i) and P(1+R/100)^6=10035…(ii)
On dividing,we get (1+R/100)^3=10025/6690=3/2.
Substituting this value in (i),we get:
P*(3/2)=6690 or P=(6690*2/3)=4460
Hence,the sum is rs.4460.

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271 75957
Q:

What is the rate of interest p.c.p.a.?

I. An amount doubles itself in 5 years on simple interest.

II. Difference between the compound interest and the simple interest earned on a certain amount in 2 years is Rs. 400.

III. Simple interest earned per annum is Rs. 2000

A) I only B) II and III only
C) All I, II and III D) I only or II and III only
 
Answer & Explanation Answer: D) I only or II and III only

Explanation:

I.P*R*5100=PR=20

 II.P1+R1002-P-P*R*2100=400=>pR2=4000000

 III.P*R*1100=2000=>PR=200000

 PR2PR=4000000200000R=20

 

Thus I only or (II and III) give answer.

 

 Correct answer is (D)

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91 60198
Q:

Find compound interest on Rs. 8000 at 15% per annum for 2 years 4 months, compounded annually

A) 2109 B) 3109
C) 4109 D) 6109
 
Answer & Explanation Answer: B) 3109

Explanation:

Time = 2 years 4 months = 2(4/12) years = 2(1/3) years.
Amount = Rs'. [8000 X (1+(15/100))^2 X (1+((1/3)*15)/100)]
=Rs. [8000 * (23/20) * (23/20) * (21/20)]
= Rs. 11109. .
:. C.I. = Rs. (11109 - 8000) = Rs. 3109.

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350 59220
Q:

A sum of money lent at compound interest for 2 years at 20% per annum would fetch Rs.482 more, if the interest was payable half yearly than if it was payable annually . The sum is

A) 10000 B) 20000
C) 40000 D) 50000
 
Answer & Explanation Answer: B) 20000

Explanation:

Let sum=Rs.x

 

C.I. when compounded half yearly = x1+101004-x=464110000

 

C.I. when compounded annually =x201002-x=1125

 464110000x-1125x=482

 

=> x=20000

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277 57931
Q:

Find the compound interest on Rs. 10,000 in 2 years at 4% per annum, the interest being compounded half-yearly.

A) 524.32 B) 624.32
C) 724.32 D) 824.32
 
Answer & Explanation Answer: D) 824.32

Explanation:

Principal = Rs. 10000; Rate = 2% per half-year; Time = 2 years = 4 half-years.
Amount == Rs. 10824.32.

 

 Rs.10000*1+21004=Rs.10000*5150*5150*5150*5150

 

 C.I. = Rs. (10824.32 - 10000) = Rs. 824.32.

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146 54831
Q:

Find the compound interest on Rs. 16,000 at 20% per annum for 9 months, compounded quarterly

A) 2422 B) 2522
C) 2622 D) 2722
 
Answer & Explanation Answer: B) 2522

Explanation:

Principal = Rs. 16000; Time = 9 months =3 quarters;
Rate = 20% per annum = 5% per quarter.
Amount = Rs. [16000 x (1+(5/100))3] = Rs. 18522.

 

 

 

CJ. = Rs. (18522 - 16000) = Rs. 2522

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86 53998
Q:

Find compound interest on Rs. 7500 at 4% per annum for 2 years, compounded annually.

A) 612 B) 712
C) 812 D) 912
 
Answer & Explanation Answer: A) 612

Explanation:

Amount = Rs [7500*(1+(4/100)2] = Rs (7500 * (26/25) * (26/25) ) = Rs. 8112.
therefore, C.I. = Rs. (8112 - 7500) = Rs. 612.

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74 53293