Arithmatical - Compound Interest

DIRECTIONS : Problems based on Interest.
5. 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.  10.5%
Solution
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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6. The difference between simple interest and compound interest on Rs.1200 for one year at 10% per annum reckoned half yearly is
  A.  Rs.2.50
  B.  Rs.3
  C.  Rs.4
  D.  Rs.3.75
Solution
S.I= Rs.(1200x10x1/100)
Rs.120.
C.I=Rs[(1200x1+5/100)² -1200]
Rs.123.
Difference= Rs.[123-120]
Rs. 3.

7. A sum of money invested at compound interest amounts to Rs.800 in 3 years and to Rs.840 in 4 years. The rate of interest per annum is
  A.   2x1/2%
  B.  4%
  C.  5%
  D.  6x2/3%
Solution
S.I. on Rs.800 for 1 year=Rs[840 - 800]
= Rs.40
Rate=(100x40/800x1)%
= 5%
8. If the simple interest on a sum of money for 2 years at 5% per annum is Rs.50, what is the compound interest on the same at the same rate and for the same time?
  A.  Rs.51.25
  B.  Rs.52
  C.  Rs.54.25
  D.  Rs.60
Solution
Sum =Rs.(50 x 100/2x5)
= Rs. 500.
Amount =[Rs.(500 x(1+5/100)²]
= Rs(500x21/20x21/20).
=Rs. 551.25
C.I= Rs. (551.25 - 500)
= Rs. 51.25
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