Correct Answer - Option 3 : 5000
Given:
Compound interest is Rs. 1,050
Rate of interest is 20%,
Compounded half-yearly for 1 year
Formula Used:
A = CI + P
A = P (1 + R/100)n,
where,
CI is compound interest
A is amount,
P is principle,
R is rate of interest,
n is total number of years
Calculation:
Compounded half-yearly,
⇒ Time = 2 × of a year
⇒ Time = 2
Rate of interest when compounded half-yearly,
⇒ R = 1/2 of actual R
⇒ R = 1/2 × 20
⇒ R = 10%
Let the principle b Rs. x,
Now using the formula and putting the value,
⇒ A = x (1 + R/100)n
⇒ x + 1,050 = x (1 + 10/100)2
⇒ x + 1,050 = x (11/10)2
⇒ x + 1,050 = x(121/100)
⇒ 1,050 = (121/100)x – x
⇒ 1,050 = 21/100 x
⇒ x = (1,050 × 100)/21
⇒ x = 5,000
∴ The principle is Rs. 5,000.