To find out how much the man needs to deposit in order to have N150,000 after three years at a compound interest rate of 25%, we can use the compound interest formula:

\[A = P \left(1 + \frac{r}{100}\right)^n\]

Where:

- \(A\) is the final amount (N150,000)

- \(P\) is the initial principal (amount deposited)

- \(r\) is the annual interest rate (25%)

- \(n\) is the number of compounding periods (3 years)

We need to solve for \(P\):

\[N150,000 = P \left(1 + \frac{25}{100}\right)^3\]

Simplify the fraction:

\[N150,000 = P \left(1 + 0.25\right)^3\]

Calculate the expression inside the parentheses:

\[N150,000 = P \cdot 1.25^3\]

\[N150,000 = P \cdot 1.953125\]

Now, solve for \(P\):

\[P = \frac{N150,000}{1.953125}\]

\[P \approx N76,800.00\]

So, the man needs to deposit approximately N76,800.00.