Question

In what time will Rs. 20,000 becomes Rs. 21,632 at 4% per annum interest compounded yearly ?

• A. 5
• B. 4
• C. 3
• D. 2

Answer 1

Answer:

D. 2

$A = P \left(1 + \frac{R}{100}\right)^n$

Where:

• $A$ = Amount after $n$ years = Rs. 21,632

• $P$ = Principal amount = Rs. 20,000

• $R$ = Rate of interest per annum = 4%

• $n$ = Time period (in years)

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Step 1: Substitute the given values into the formula
$21,632 = 20,000 \left(1 + \frac{4}{100}\right)^n$

Step 2: Simplify the term inside the bracket
$21,632 = 20,000 (1 + 0.04)^n$
$21,632 = 20,000 (1.04)^n$

Step 3: Divide both sides by 20,000 to isolate the exponential term
$\frac{21,632}{20,000} = (1.04)^n$
$1.0816 = (1.04)^n$

Step 4: Express 1.0816 as a power of 1.04
Since $(1.04) \times (1.04) = 1.0816$, we can write:
$(1.04)^2 = (1.04)^n$

Comparing the exponents, we get:
$n = 2$

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Time Required: 2 Years