Question

If at same rate of interest, in 2 years, the simple interest is ₹44 and compound interest is ₹45, then what is the principal (in ₹)?

• A. 488
• B. 477
• C. 484
• D. 479

Answer 1

Answer:

C. 484

Let principal = P, rate = R%

Simple Interest (2 years)

$SI = \frac{PR \times 2}{100} = 44$

$\frac{PR}{100} = 22 \quad ...(1)$

Compound Interest (2 years)

$CI = P\left(1 + \frac{R}{100}\right)^2 - P = 45$

For 2 years:
$CI = SI + \frac{P R^2}{100^2}$

So,
$45 = 44 + \frac{P R^2}{10000}$

$\frac{P R^2}{10000} = 1$

$P R^2 = 10000 \quad ...(2)$

Use (1)

From (1):

PR = 2200

Square it:
$P^2 R^2 = 2200^2$

$P^2 R^2 = 4,840,000$
Divide with (2)

$PR^2 = 10000$

Divide:
$\frac{P^2 R^2}{PR^2} = \frac{4840000}{10000}$
P = 484

Final Answer: ₹484