In what time will a sum of Rs. 800 at 5% p.a. C.I. amount to Rs. 882?a...
Given:
Principal amount (P) = Rs. 800
Rate of interest (R) = 5% p.a.
Compound interest (CI) = Rs. 882 - Rs. 800 = Rs. 82
Formula for Compound Interest:
CI = P(1 + R/100)^n - P
Where, n is the number of years
Calculation:
Using the given values, we can rewrite the formula as:
82 = 800(1 + 5/100)^n - 800
82 = 8(21/20)^n
82/8 = (21/20)^n
10.25 = (21/20)^n
To solve for n, we can take the logarithm of both sides:
log(10.25) = log((21/20)^n)
log(10.25) = n * log(21/20)
n = log(10.25) / log(21/20)
n ≈ 1.999
Conclusion:
Therefore, the sum of Rs. 800 at 5% p.a. compound interest will amount to Rs. 882 in approximately 2 years. So, the correct answer is option D.