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 Compound Interest Questions

Popular Latest Rated Important Formulae

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:

Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:

A) Rs.1550 B) Rs.1650
C) Rs,1750 D) Rs.1850
 
Answer & Explanation Answer: C) Rs,1750

Explanation:

C.I.= Rs.[4000*(1+10/100)^2-4000]

 =Rs.840

sum=Rs.(420 * 100)/3*8=Rs.1750

 

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23 14427
Q:

A sum is being lent at 20 % per annum compound interest.what is the ratio of increase in amount of 4th year to 5th year?

A) 4:5 B) 5:4
C) 5:6 D) can't be determined
 
Answer & Explanation Answer: C) 5:6

Explanation:

 

P1+r1004P1+r1005=11+r100 =100100+r=100120=56 

 

                

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48 13526
Q:

The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is

A) 6.06% B) 6.07%
C) 6.08% D) 6.09%
 
Answer & Explanation Answer: D) 6.09%

Explanation:

Amount of Rs. 100 for 1 year

when compounded half-yearly = Rs.[100*(1+3/100)^2]=Rs.106.09

Effective rate=(106.09-100)%=6.09%

 

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9 12777
Q:

If you deposit $5000 into an account paying 6% annual interest compounded monthly, how long until there is $8000 in the account?

A) 6.9 B) 7.9
C) 8.9 D) 9.9
 
Answer & Explanation Answer: B) 7.9

Explanation:

 

 

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

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16 12150
Q:

What will be compounded amount?
I. Rs. 200 was borrowed for 192 months at 6% compounded annually.
II. Rs. 200 was borrowed for 16 years at 6%.

A) I alone sufficient while II alone not sufficient to answer B) II alone sufficient while I alone not sufficient to answer
C) Either I or II alone sufficient to answer D) Both I and II are not sufficient to answer
 
Answer & Explanation Answer: C) Either I or II alone sufficient to answer

Explanation:

 I. Amount = Rs.200*1+610016

 

II. Amount =Rs200*1+610016

 

Thus, I as well as II gives the answer.

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2 12038
Q:

Compound interest earned on a sum for the second and the third years are Rs.1200 and Rs.1440 respectively. Find the rate of interest ?

A) 20% p.a B) 15% p.a
C) 18% p.a D) 24% p.a
 
Answer & Explanation Answer: A) 20% p.a

Explanation:

Rs.1440 - 1200 = Rs.240 is the interest on Rs.1200 for one year.

Rate of interest = (100 x 240) / (1200) = 20% p.a

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7 11917
Q:

Albert invested an amount of Rs.8000 in a fixed deposit scheme for 2 years at compound interest rate 5 p.c.p.a. How much amount will Albert get on maturity of the fixed deposit ?

A) Rs.8600 B) Rs.8830
C) Rs.8500 D) Rs.8820
 
Answer & Explanation Answer: D) Rs.8820

Explanation:

Amount

=Rs.[8000x(1+5/100)²]

= Rs.[8000 x 21/20x21/20]

= Rs.8820. 

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4 11221
Q:

Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received Rs.550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received Rs.605 as interest. What was the value of his total savings before investing in thesetwo bonds?

A) Rs.2543 B) Rs.2534
C) Rs.2546 D) Rs.2750
 
Answer & Explanation Answer: D) Rs.2750

Explanation:

 

Shawn received an extra amount of (Rs.605 – Rs.550) Rs.55 on his compound interest paying bond as the interest that he received in the first year also earned interest in the second year.

 

The extra interest earned on the compound interest bond = Rs.55

 

The interest for the first year =550/2 = Rs.275

 

Therefore, the rate of interest =55275*100= 20% p.a.

 

20% interest means that Shawn received 20% of the amount he invested in the bonds as interest.

 

If 20% of his investment in one of the bonds = Rs.275, then his total investment in each of the  bonds =27520*100 = 1375. 

As he invested equal sums in both the bonds, his total savings before investing = 2 x 1375 =Rs.2750.

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