On what sum will the difference between the simple and compound interest for 3 years if the rate of interest is 10% p.a. is ₹ 232.50?
Solution:
Consider sum (P) = ₹ 100
Rate (r) = 10% p.a.
Period (n) = 3 years
We know that
A = P (1 + r/100)n
Substituting the values
= 100 (1 + 10/100)3
By further calculation
= 100 × 11/10 × 11/10 × 11/10
= ₹ 133.10
Here, CI = A – P
Substituting the values
= 133.10 – 100
= ₹ 33.10
So the simple interest = PRT/100
Substituting the values
= (100 × 10 × 3)/ 100
= ₹ 30
Difference = 33.10 – 30 = ₹ 3.10
Here if the difference is ₹ 3.10 then sum = ₹ 100
If the difference is ₹ 232.50 then sum = (100 × 232.50)/ 3.10
Multiplying and dividing by 100
= (100 × 23250)/ 310
= ₹ 7500
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