A sum of money is lent out at compound interest for two years at 20% p.a., CI being reckoned yearly. If the same sum of money is lent out at compound interest at same rate percent per annum, CI being reckoned half-yearly, it would have fetched ₹ 482 more by way of interest. Calculate the sum of money lent out.
Solution:
It is given that
Sum = ₹ 100
Rate = 20% p.a. or 10% half-yearly
Period = 2 years or 4 half-years
Case 1 – When the interest is reckoned yearly
A = P (1 + r/100)n
Substituting the values
= 100 (1 + 20/100)2
By further calculation
= 100 × 6/5 × 6/5
= ₹ 144
We know that
CI = A – P
Substituting the values
= 144 – 100
= ₹ 44
Case 2 – When the interest is reckoned half-yearly
A = P (1 + r/100)n
Substituting the values
= 100 (1 + 10/100)4
By further calculation
= 100 × 11/10 × 11/10 × 11/10 × 11/10
= ₹ 146.41
We know that
CI = A – P
Substituting the values
= 146.41 – 100
= ₹ 46.41
So the difference between two CI = 46.41 – 44 = ₹ 2.41
If the difference is ₹ 2.41 then sum = ₹ 100
If the difference is ₹ 482 then sum = (100 × 482)/ 2.41
Multiplying and dividing by 100
= (100 × 482 × 100)/ 241
= ₹ 20000
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