Securities future value is Rs 1,000,000 and present value of securities is Rs 500,000 with an interest rate of 4.5%, ‘N’ will be

The correct answer is A. 16.7473 years.

The formula for calculating the number of years (N) to reach a future value (FV) given a present value (PV), an interest rate (r), and a compounding frequency (m) is:

$N = \dfrac{\ln(FV/PV)}{\ln(1 + r/m)}$

In this case, we are given that FV = 1,000,000, PV = 500,000, r = 4.5%, and m = 12 (monthly compounding). Substituting these values into the formula, we get:

$N = \dfrac{\ln(1,000,000/500,000)}{\ln(1 + 0.045/12)} = 16.7473$ years

Option B is incorrect because 0.0304 months is not a valid number of years. Option C is incorrect because 15.7473 years is not a valid number of years. Option D is incorrect because 0.7575 years is not a valid number of years.