The compound interest on a sum for 2 years is Rs 832 and the simple interest…
2023
The compound interest on a sum for 2 years is Rs 832 and the simple interest on the same sum for the same period is Rs 800. The difference between the compound and simple interest for 3 years will be
- A.
Rs 48
- B.
Rs 80
- C.
Rs 66.56
- D.
Rs 98.56
Attempted by 4 students.
Show answer & explanation
Correct answer: D
Solution:
Simple interest for 2 years = Rs 800, so simple interest per year = Rs 400. Therefore Pr = 400 (where P is principal and r is annual rate in decimal).
Compound interest for 2 years = Rs 832. The excess of compound over simple interest for 2 years is 832 - 800 = Rs 32, which equals Pr^2. So Pr^2 = 32.
From Pr = 400 and Pr^2 = 32 we get r = (Pr^2)/(Pr) = 32/400 = 0.08 = 8% per year.
Difference between compound and simple interest for 3 years can be written as 3Pr^2 + Pr^3 (this comes from expanding (1+r)^3 - 1 and subtracting 3r).
Compute Pr^2 = 32 and Pr^3 = Pr^2 * r = 32 * 0.08 = 2.56.
So the total difference = 3*32 + 2.56 = 96 + 2.56 = 98.56.
An alternative view: the extra in the second year is Rs 32; the extra in the third year equals r times the compound interest for 2 years = 0.08*832 = 66.56; total extra = 32 + 66.56 = 98.56.
Answer: Rs 98.56