1.

The difference between simple and compound interest on a certain sum of money for 2 years at 4 per cent per annum is Rs. 1. The sum of money is1). Rs. 6002). Rs. 6253). Rs. 5604). Rs. 650

Answer»

As we know-

$(CI\; = \;\left[ {P \times {{\left( {1 + \frac{R}{{100}}} \right)}^T}} \right] - P)$

And SI = (P × R × T)/100

Where, P = principal AMOUNT, R = % rate of interest, T = time period in years, CI = compound interest and SI = simple interest

Here, let the principal amount be Rs. P.

Rate of interest = 4% PER annum

Total time = 2 years

As per given data-

Difference between the compound interest and simple interest is Rs. 1

$(\begin{array}{l} \Rightarrow \;\left[ {P \times {{\left( {1 + \frac{4}{{100}}} \right)}^2}} \right] - P\; - \;\frac{{P \times \;4 \times \;2}}{{100}}\; = \;1\\ \Rightarrow \frac{{P \times 104 \times 104}}{{100 \times 100}} - P - \frac{{8P}}{{100}} = 1\\ \Rightarrow \frac{{{{104}^2}P - {{100}^2}P - 800P}}{{100 \times 100}} = 1\;\end{array})$

⇒ 16P = 10000

⇒ P = 10000/16 = 625

∴ Principal amount = 625 Rs.


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