An investment of GHS 10,000 is being considered for two options. Option A offers an 8% annual interest rate compounded quarterly. Option B offers a 7.5% annual interest rate compounded monthly. Both i

The formula for compound interest is $A = P \left(1 + \frac{r}{n}\right)^{nt}$.
For Option A:
$P = \text{GHS } 10,000$
$r = 8\% = 0.08$
$n = 4$ (compounded quarterly)
$t = 5$ years

The final amount for Option A is $\boxed{\text{GHS } \textbf{14859.47}}$.

For Option B:
$P = \text{GHS } 10,000$
$r = 7.5\% = 0.075$
$n = 12$ (compounded monthly)
$t = 5$ years

The final amount for Option B is $\boxed{\text{GHS } \textbf{14499.48}}$.

Profit for Option A = Final Amount - Principal

Profit for Option B = Final Amount - Principal

Option A yields more profit.
Difference in profit = $P_A - P_B = 4859.47 - 4499.48 = 359.99$
Option A yields more profit by $\boxed{\text{GHS } \textbf{359.99}}$.

The formula given is $t = \frac{\ln(2)}{n \ln\left(1+\frac{r}{n}\right)}$.
For Option A:
$r = 0.08$
$n = 4$

It would take approximately $\boxed{\textbf{8.75 years}}$ for the investment to double.

Generally, for a given principal, annual interest rate, and time period, a higher compounding frequency (more times per year) leads to a higher final amount. This is because interest is calculated and added to the principal more often, allowing subsequent interest calculations to be based on a larger principal, leading to greater overall growth.