Raja's Age and Life Expectancy
Raja is currently 45 years old and resides on planet X, where the specific expectation of life is different from Earth. This means that the average lifespan on planet X may be shorter or longer than on Earth.

Investment and Compound Interest
To ensure a comfortable and financially secure retirement, Raja needs to start investing a certain amount annually. With a compound interest rate of 3% per annum, his investments will grow over time.

Determining the Annual Investment
To calculate the annual investment amount, we need to consider Raja's expected lifespan and the desired retirement corpus. Let's assume that Raja expects to live until the age of 85. So, he has 40 more years until retirement (85 - 45 = 40).

Retirement Corpus Calculation
To determine the retirement corpus, we can use the future value of an ordinary annuity formula. The formula is: FV = P * [(1 + r)^n - 1] / r, where FV is the future value, P is the annual investment, r is the interest rate, and n is the number of years.

Substituting the Values
In this case, Raja wants to calculate the annual investment (P). Let's assume that he desires a retirement corpus of $1,000,000.

FV = $1,000,000
r = 3% or 0.03
n = 40

Calculating the Annual Investment
To find the annual investment amount, we rearrange the formula:

P = FV * r / [(1 + r)^n - 1]

P = $1,000,000 * 0.03 / [(1 + 0.03)^40 - 1]

P ≈ $1,000,000 * 0.03 / [1.03^40 - 1]

P ≈ $1,000,000 * 0.03 / [2.208 - 1]

P ≈ $1,000,000 * 0.03 / 1.208

P ≈ $1,000,000 * 0.0248

P ≈ $24,800

Conclusion
To ensure a financially secure retirement, Raja should invest approximately $24,800 annually. This investment, with a 3% compound interest rate per annum, will help him accumulate a retirement corpus of $1,000,000 by the time he reaches the age of 85. It is important to note that this calculation assumes a constant interest rate and annual investment, and does not take into account any additional factors such as inflation or fluctuations in the market.