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 least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is:

A) 3 B) 4
C) 5 D) 6
 
Answer & Explanation Answer: B) 4

Explanation:

 

 P1+20100n>2P65n>2

 65×65×65×65>2

 

so, answer is 4 years

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16 10881
Q:

Rs 1000 is being  charged at 50% per annum. what is the interest for 3rd year at compound interest?

A) 1122 B) 1025
C) 1125 D) 625
 
Answer & Explanation Answer: C) 1125

Explanation:

Total amount for two years =  1000×1.52=2250

 Now , interest for third year = 2250×50×1100=1125

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16 10748
Q:

At a certain rate of interest the compound interest of 3 years and simple interest of 5 years for certain sum of money is respectively Rs. 1513.2 and Rs. 2400. Find the common rate of interest per annum ?

A) 5% B) 6%
C) 4% D) 3%
 
Answer & Explanation Answer: A) 5%

Explanation:

Given compound interest for 3 years = Rs. 1513.2

 

and simple interest for 5 years = Rs. 2400

 

Now, we know that  C.I = P1+R100n - 1

 

=> 1513.2 = P1+R1003 - 1 ...........(A)

 

And S.I = PTR/100

 

=> 2400 = P5R/100 ..................(B)

 

By solving (A) & (B), we get

 

R = 5%.

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17 10338
Q:

Sonika invested an amount of Rs.5800 for 2 years. At what rate of compound interest will she get an amount of Rs.594.50 at the end of 2 years ?

A) 6.5% B) 6%
C) 5% D) 4.5%
 
Answer & Explanation Answer: C) 5%

Explanation:

C.I = P1+r100t-1

 

594.5 = 58001+r1002-1

 594.55800+1=1+r1002

 

r100=1.05-1=0.05=> r = 5 % .

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13 10214
Q:

Mr. Gupta borrowed a sum of money on compound interest. What will be the amount to
be repaid if he is repaying the entire amount at the end of 2 years?
I. The rate of interest is 5 p.c.p.a.
II. Simple interest fetched on the same amount in one year is Rs. 600.
III. The amount borrowed is 10 times the simple interest in 2 years.

A) .I only B) III only
C) I or II D) II and Either I or III only
 
Answer & Explanation Answer: D) II and Either I or III only

Explanation:

   I. gives, Rate = 5% p.a.

 

 II. gives, S.I. for 1 year = Rs. 600.

 

III. gives, sum = 10 x (S.I. for 2 years).

 


 Now I, and II give the sum.


 For this sum, C.I. and hence amount can be obtained.


 Thus, III is redundant.


 Again, II gives S.I. for 2 years = Rs. (600 x 2) = Rs. 1200.


 Now, from III, Sum = Rs. (10 x 1200) = Rs . 12000.


Thus,Rate =100*12002*12000 =5%


Thus, C.I. for 2 years and therefore, amount can be obtained.


Thus, I is redundant.



Hence, I or III redundan
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5 9732
Q:

The minimum number of half years in which a sum of money kept at 60% compound interest will be quadrupled is ?

A) 2 B) 4
C) 3 D) 6
 
Answer & Explanation Answer: D) 6

Explanation:

Let us assume Amount be 100 Rs and we calculate in CI

 First year 60% of 100 = 60 amount (100+60) is 160

 Second year 60% of 160 = 96 amount (160+96) is 256

 Third year 60% of 256 =153.6 amount (256+153.6) is 409.6

 Here the Amount of 100 Rs is quadrapled in 3 years.

 One year contains 2 half years

 Three year has 6 half years.

 Therefore,  It takes 6 half years.

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14 9606
Q:

There is 50% increase in an amount in 5 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate ?

A) Rs. 5422 B) Rs. 5489
C) Rs. 3972 D) Rs. 6145
 
Answer & Explanation Answer: C) Rs. 3972

Explanation:

Let p = Rs. 100.

Then, S.I is Rs. 50 and time = 5 years. 

 R = 100×50100×5= 10% p.a.

 

Now, p = Rs. 12,000 , T = 3 years and R = 10% p.a.


C.I. = Rs. 12000×1+101003-1= Rs. 3972

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7 9597
Q:

If you deposit $8000 into an account paying 7% annual interest compounded quarterly, how long until there is $12400 in the account?

A) 2.3 B) 3.3
C) 4.3 D) 6.3
 
Answer & Explanation Answer: D) 6.3

Explanation:

 

 

FV=P(1+r/n)^nt

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