A trader borrows N600,000 from a moneylender at a rate of 15% per annum simple interest. Calculate the interest and the total amount the trader will pay altogether after five months.

The principal amount borrowed ($P$) is 600,000.
The annual interest rate ($R$) is 15%, which is 0.15 in decimal form.
The time period ($T$) is 5 months. Since the interest rate is annual, convert the time to years:

$$T = \frac{5}{12} \text{ years}$$

The formula for simple interest ($I$) is:

$$I = P \times R \times T$$

Substitute the values:

$$I = 600,000 \times 0.15 \times \frac{5}{12}$$ $$I = 90,000 \times \frac{5}{12}$$ $$I = \frac{450,000}{12}$$ $$I = 37,500$$

The interest the trader must pay is 37,500.

The total amount ($A$) to be paid altogether is the principal plus the interest:

$$A = P + I$$

Substitute the values:

$$A = 600,000 + 37,500$$ $$A = 637,500$$

The total amount the trader will pay altogether is 637,500.

a) The interest he must pay after five months is:

$$\boxed{37,500}$$

b) The total amount the trader will pay altogether is:

$$\boxed{637,500}$$