The difference in simple interest and compound interest on a certain s

1.	The difference in simple interest and compound interest on a certain sum of money at 6 2/3 % per annum for 3 years in Rs. 46. Determine the sum.
Answer» Given, Time = 3 years Rate = 6 2/3 % per annum = 20/3% Let principal = Rs P Compound Interest (CI) – Simple Interest (SI) = Rs 46 C.I – S.I = Rs 46 By using the formula, P [(1 + R/100)ⁿ – 1] – (PTR)/100 = 46 P [(1 + 20/3×100)³ – 1] – (P(3)(20/3))/100 = 46 P[(1 + 20/300)³ – 1] – P/5 = 46 P[721/3375] – P/5 = 46 721/3375P – 1/5P = 46 (721P-675P)/3375 = 46 46P = 46 × 3375 46P = 46 × 3375/46 = 3375 ∴ The sum is Rs 3375.

The difference in simple interest and compound interest on a certain sum of money at 6 2/3 % per annum for 3 years in Rs. 46. Determine the sum.

Answer»

Given,

Time = 3 years

Rate = 6 2/3 % per annum = 20/3%

Let principal = Rs P

Compound Interest (CI) – Simple Interest (SI) = Rs 46

C.I – S.I = Rs 46

By using the formula,

P [(1 + R/100)ⁿ – 1] – (PTR)/100 = 46

P [(1 + 20/3×100)³ – 1] – (P(3)(20/3))/100 = 46

P[(1 + 20/300)³ – 1] – P/5 = 46

P[721/3375] – P/5 = 46

721/3375P – 1/5P = 46

(721P-675P)/3375 = 46

46P = 46 × 3375

46P = 46 × 3375/46

= 3375

∴ The sum is Rs 3375.