A sum of money is borrowed at compound interest payable annually. The interests for the 2nd and 3rd year are Rs.330 and Rs.335 respectively. Find the sum.
Answers
Compound Interest
Let P be the sum and r% be the rate of compound interest.
1st year:
Sum = P
Rate of interest = r%
Amount = P (1 + r/100)
2nd year:
Sum = P (1 + r/100)
Rate of interest = r%
Amount = P (1 + r/100)²
Interest = P (1 + r/100)² - P (1 + r/100)
= P (1 + r/100) (1 + r/100 - 1)
= P (1 + r/100) * r/100
==> P (1 + r/100) * r/100 = 330 .....(i)
3rd year:
Sum = P (1 + r/100)²
Rate of interest = r%
Amount = P (1 + r/100)³
Interest = P (1 + r/100)³ - P (1 + r/100)³
= P (1 + r/100)² (1 + r/100 - 1)
= P (1 + r/100)² * r/100
==> P (1 + r/100)² * r/100 = 335 .....(ii)
Dividing (ii) by (i), we get
1 + r/100 = 335/330
Or, r/100 = 5/330 = 1/66
Or, r = 100/66
Or, r = 50/33
Putting r = 55/33 in (i), we get
P {1 + (50/33)/100} * (50/33)/100 = 330
Or, P (1 + 1/66) * 1/66 = 330
Or, P * 67/66 * 1/66 = 330
Or, P = (330 * 66 * 66)/67
Or, P = 21454.93
Hence, the sum is Rs. 21454.93
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