Question

The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is​

Answer 1

Answer:

P = 625

Step-by-step explanation:

Solution:-

Let the principle amount be 'P'

The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is ₹ 1.

Compound intrest = P[( 1 + i)ⁿ-1]

Simple intrest = P × i × T

Difference = 1

P[( 1 + i)ⁿ-1] - ( P × i × T ) = 1

P = ?

N = 2

R = 4%

Simple intrest = P × 4% × 2 = 8P/100

Compound intrest = P[( 1 + 0.04)²-1] = 0.0816P

[(1.04)²-1] = 0.0816

Difference =

$\frac{8P}{100} - 0.0816P = 1\\\\\frac{8.16P - 8P}{100} = 1\\\\0.16P = 100\\\\=> P = \frac{100}{0.16}\\\\P = 625$

Answer 2

Step-by-step explanation:

Solution:-

Let the principle amount be 'P'

The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is ₹ 1.

Compound intrest = P[( 1 + i)ⁿ-1]

Simple intrest = P × i × T

Difference = 1

P[( 1 + i)ⁿ-1] - ( P × i × T ) = 1

P = ?

N = 2

R = 4%

Simple intrest = P × 4% × 2 = 8P/100

Compound intrest = P[( 1 + 0.04)²-1] = 0.0816P

[(1.04)²-1] = 0.0816

Difference =

\begin{gathered}\frac{8P}{100} - 0.0816P = 1\\\\\frac{8.16P - 8P}{100} = 1\\\\0.16P = 100\\\\= > P = \frac{100}{0.16}\\\\P = 625\end{gathered}1008P−0.0816P=11008.16P−8P=10.16P=100=>P=0.16100P=625