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 difference between the compound interest and the simple interest on a certain sum at 12% p.a. for two years is Rs.90. What will be the value of the amount at the end of 3 years?

A) 8560 B) 8673
C) 8746 D) 8780.80
 
Answer & Explanation Answer: D) 8780.80

Explanation:

when interest is reckoned using compound interest, interest being compounded annually. The difference in the simple interest and compound interest for two years is on account of the interest paid on the first year's interest  Hence 12% of simple interest = 90 => simple interest =90/0.12 =750.

As the simple interest for a year = 750 @ 12% p.a., the principal =750/0.12 = Rs.6250.

If the principal is 6250, then the amount outstanding at the end of 3 years = 6250 + 3(simple interest on 6250) + 3 (interest on simple interest) + 1 (interest on interest on interest) = 6250 +3(750) + 3(90) + 1(10.80) = 8780.80.

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Q:

What annual payment will discharge a debt of Rs.7620 due in 3years at1623 % per annum interest?

A) 5430 B) 4430
C) 3430 D) 2430
 
Answer & Explanation Answer: C) 3430

Explanation:

Let each installment be Rs.x. Then, 

(P.W. of Rs.x due 1 year hence) + (P.W of Rs.x due 2 years hence) + (P.W of Rs. X due 3 years hence) = 7620.

 

x1+503x100+x1 +503x1002+x1 +503x1003 = 7620

 

 6x7+36x49+216x343=7620

 

 294x + 252x + 216x = 7620 x 343

 

 => x = 3430

 

 Amount of each installment = Rs.3430

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Q:

Divide Rs. 1301 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 4% per annum.

A) Rs.625 B) Rs.626
C) Rs.286 D) Rs.627
 
Answer & Explanation Answer: A) Rs.625

Explanation:

Let the two parts be Rs. x and Rs. (1301 - x).

 x1+41007=1301-x1+41009

 x1301-x=1+41002=2625*2526

 

=> 625x=676(1301-x) 

1301x=676 x 1301x=676.
So,the parts are rs.676 and rs.(1301-676)i.e rs.676 and rs.625

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Q:

The difference between the compound interest and simple interest on a certain sum at 10% per annum for 2 years is Rs. 631. Find the sum.

A) 60100 B) 61100
C) 62100 D) 63100
 
Answer & Explanation Answer: D) 63100

Explanation:

Let the sum be Rs. x. Then,
C.I. = x ( 1 + ( 10 /100 ))^2 - x = 21x / 100 ,
S.I. = (( x * 10 * 2) / 100) = x / 5
(C.I) - (S.I) = ((21x / 100 ) - (x / 5 )) = x / 100
( x / 100 ) = 632 * x = 63100.
Hence, the sum is Rs.63,100.

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27 23810
Q:

The difference between the compound interest and the simple interest accrued on an amount of Rs. 18,000 in 2 years was Rs. 405. What was the rate of interest p.c.p.a. ?

A) 12% B) 13%
C) 14% D) 15%
 
Answer & Explanation Answer: D) 15%

Explanation:

Let the rate be R% p.a. Then,

 

18001+R1002-1800-1800*R*2100=405

1800100+R210000-1-2R100=405

 1800100+R2-10000-200R10000=405

95*R2=405 R2=405*59=225R=15 
Rate = 15%.

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Q:

The principal that amounts to Rs.4913 in 3 years at 413% per annum compound interest compounded annually is

A) Rs.3096 B) Rs.4076
C) Rs.4085 D) Rs.4096
 
Answer & Explanation Answer: D) Rs.4096

Explanation:

principal = A=4913,T=3, R=413

P=A1+R100T

 

 = Rs.4096

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Q:

The population of a town was 3600 three years back. It is 4800 right now. What will be the population three years down the line, if the rate of growth of population has been constant over the years and has been compounding annually?

A) Rs.600 B) Rs,6400
C) Rs.6500 D) Rs.6600
 
Answer & Explanation Answer: B) Rs,6400

Explanation:

 

The population grew from 3600 to 4800 in 3 years. That is a growth of 1200 on 3600 during three year span.

 

Therefore, the rate of growth for three years has been constant.

 

The rate of growth during the next three years will also be the same.

 

Therefore, the population will grow from 4800 by 4800*13= 1600

 

Hence, the population three years from now will be 4800 + 1600 = 6400

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Q:

The present worth of Rs.169 due in 2 years at 4% per annum compound interest is

A) Rs.156.25 B) Rs.150
C) Rs.140 D) Rs125.25
 
Answer & Explanation Answer: A) Rs.156.25

Explanation:

 

Present Worth

 

=P1+R1002

 

=1691+41002

 

= Rs.156.25

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