Calculate the time taken for an investment of GH¢312.50 to grow to GH¢500.00 at an annual interest rate of 4%.

The interest earned ($I$) is the difference between the final amount ($A$) and the principal ($P$).

$$I = A - P$$ $$I = \text{GH¢}500.00 - \text{GH¢}312.50$$ $$I = \text{GH¢}187.50$$

The formula for simple interest is $I = PRT$, where $P$ is the principal, $R$ is the annual interest rate, and $T$ is the time in years.
Given:
$I = \text{GH¢}187.50$
$P = \text{GH¢}312.50$
$R = 4\% = 0.04$
We need to find $T$.

$$187.50 = 312.50 \times 0.04 \times T$$

$$187.50 = 12.5 \times T$$ $$T = \frac{187.50}{12.5}$$ $$T = 15$$

The time taken is 15 years.

The final answer is $\text{15 years}$.