Arithmatical - Compound Interest

DIRECTIONS : Problems based on Interest.
13. In what time will Rs.1000 become Rs.1331 at 10% per annum compounded annually?
  A.  2 years
  B.  3 years
  C.  4 years
  D.  7 years
Solution
Principal= Rs.1000;
Amount= Rs.1331;
Rate= Rs.10%p.a.
Let the time be n years.Then
[1000(1+10/100)Λn;]
= 1331.
= (1331/1000)
= (11/10)³
Therefore n = 3 years.
14. 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%
Solution
Amount of Rs.100 for 1 year when compounded half yearly
= Rs.[100 x (1+3/100)2]
= Rs. 106.09%.
Effective rate= (106.09 - 100)%
= Rs. 6.09%.

15. What will be the difference between simple interest and compound interest @10% per annum on a sum of Rs. 1000 after 4 years?
  A.  Rs. 31
  B.  Rs. 32.10
  C.  Rs. 40.40
  D.  Rs. 64.10
Solution
S.I. =Rs(1000x10x4 / 100)
= Rs.400.
C.I.=Rs.[1000x(1x10/100)4-1000]
= Rs. 464.10
∴ Difference = Rs.(464.10 - 400)
= Rs. 64.10
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