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:

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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Q:

There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate

A) Rs.4972 B) Rs.3972
C) Rs.5972 D) Rs.2972
 
Answer & Explanation Answer: B) Rs.3972

Explanation:

 

Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.

 

R=100*60100*6 =10% p.a

 

Now, P = Rs. 12000. T = 3 years and R = 10% p.a.

 

C.I=Rs.12000*1+101003-1
       =Rs.3972

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Q:

The difference between compound interest and simple interest on a sum for two years at 8% per annum, where the interest is compounded annually is Rs.16. if the interest were compounded half yearly , the difference in two interests would be nearly

A) Rs.24.64 B) Rs.21.85
C) Rs.16 D) Rs.16.80
 
Answer & Explanation Answer: A) Rs.24.64

Explanation:

For 1st year S.I =C.I.

 

Thus, Rs.16 is the S.I. on S.I. for 1 year, which at 8% is thus Rs.200

 

i.e S.I on the principal for 1 year is Rs.200

 

Principle = Rs.100*2008*1 = Rs.2500

 

Amount for 2 years, compounded half-yearly

 Rs.2500*1+41004=Rs.2924.4

 

C.I = Rs.424.64

 

Also, S.I=Rs.2500*8*2100=Rs.400

 

Hence, [(C.I) - (S.I)] = Rs. (424.64 - 400) = Rs.24.64

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Q:

If the simple interest on a sum of money at 5% per annum for 3 years is Rs. 1200, find the compound interest on the same sum for the same period at the same rate.

A) 1261 B) 1271
C) 1281 D) 1291
 
Answer & Explanation Answer: A) 1261

Explanation:

Clearly, Rate = 5% p.a., Time = 3 years, S.I.= Rs. 1200. . .
So principal=RS [100*1200]/3*5=RS 8000
Amount = Rs. 8000 x [1 +5/100]^3 - = Rs. 9261.
.. C.I. = Rs. (9261 - 8000) = Rs. 1261.

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Q:

What is the difference between the compound interests on Rs. 5000 for 1 1/2  years at 4% per annum compounded yearly and half-yearly?

A) 2.04 B) 3.04
C) 4.04 D) 5.04
 
Answer & Explanation Answer: A) 2.04

Explanation:

C.I. when interest
compounded yearly=rs.[5000*(1+4/100)(1+1/2*4/100)]

= Rs. 5304.

C.I. when interest is
compounded half-yearly=rs.5000(1+2/100)^3

= Rs. 5306.04
Difference = Rs. (5306.04 - 5304) = Rs. 2.04

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Q:

A certain sum amounts to Rs.7350 in 2 years and to Rs.8575 in 3 years.find the sum and rate percent

A) 3400 B) 4400
C) 5400 D) 6400
 
Answer & Explanation Answer: C) 5400

Explanation:

Interest for 1 year is the same whether it's simple interest or the compound interest.

Now interest of third year = 8575 - 7350 = 1225; means principal for this interest is 7350 if comound interest is takenIf 7350 is the principal interest = 1225

if 100 is the principal interest =(1225/7350) * 100 = 50/3 %

When a thing increases for two successive times the overall increase on initial amount = a + b + (a * b)/100

Therefore overall interest for two years = 50/3 + 50/3 + [(50/3)*(50/3)]/100 = 325/9 %

Therefore amount after 2 years = 100 + 325/9 = 1225/9

If 1225/9 is the amount principal =100

if 7350 is the amount principal =(900/1225)*7350 =5400

So sum = 5400; Rate = 50/3 %

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Q:

On a sum of money, the simple interest for 2 years is Rs. 660,while the compound interest is Rs.696.30,the rate of interest being the same in both the cases. The rate of interest is

A) 10% B) 11%
C) 12% D) 13%
 
Answer & Explanation Answer: B) 11%

Explanation:

Difference in C.I and S.I for 2 years

= Rs(696.30-660)

=Rs. 36.30.

 

S.I for one years = Rs330.

S.I on Rs.330 for 1 year =Rs. 36.30 

 

Rate

= (100x36.30/330x1)%

= 11%

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Q:

The difference between the simple interest on a certain sum at the rate of 10%per annum for 2 years and compound interest which is compounded every 6 months is Rs.124.05. what is the principal sum

A) Rs.6000 B) Rs.8000
C) Rs.12000 D) none of these
 
Answer & Explanation Answer: B) Rs.8000

Explanation:

Compound Interest on P at 10% for 2 years when interest is compounded half-yearly

 

=P1+R21002T-P=P1+1204-P=P21204-P

 

Simple Interest on P at 10% for 2 years = PRT100=P×10×2100=P5

 

Given that difference between compound interest and simple interest = 124.05

 P*21204-P-P5=124.05

 

=>P21204-1-15=124.05

 P=8000

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