Find the principal if compound interest for 2 years is Rs. 4,070 and rate of interest is 5.55% per annum
1. Rs. 35,540
2. Rs. 35,640
3. Rs. 45,440
4. Rs. 36,450
1. Rs. 35,540
2. Rs. 35,640
3. Rs. 45,440
4. Rs. 36,450
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Correct Answer – Option 2 : Rs. 35,640
Given:
Compound interest = Rs. 4,070
Rate = 5.55%
Time = 2 years
Concept used:
11.11% = 1/9
Formula used:
C.P = P{(1 + R/100)T – 1}
Where,
C.P → Compound interest
P → Principal
R → Rate
T → Time
Calculations:
11.11% = 1/9
⇒ (11.11%)/2 = 1/(9 × 2)
⇒ 5.55% = 1/18
Now, C.I. = P{(1 + R/100)T – 1}
⇒ 4070 = P{(1 + 5.55/100)2 – 1)}
⇒ 4070 = P {(1 + 1/18)2 – 1}
⇒ 4070 = P{(19/18 × 19/18) – 1}
⇒ 4070 = P{(361 – 324)/324}
⇒ 4070 = P × (37/324)
⇒ P = (4070 × 324)/37
⇒ 110 × 324
⇒ Rs. 35,640
∴ The principal is Rs. 35,640