To determine the rate of return for the investment, we'll follow these steps:

1. Understanding the Inputs:

• Monthly deposit (PMT): $2500
• Duration: 5 years
• Annual interest rate (r): 9.8% compounded semi-annually
• Compounding frequency: Semi-annually (2 times a year)

2. Interest Rate Adjustments:

Since the interest is compounded semi-annually, we need to adjust the annual interest rate for semi-annual compounding.

The semi-annual interest rate $i_s$ is: $i_s = \frac{9.8\%}{2} = 4.9\% = 0.049$

The number of compounding periods for 5 years, given semi-annual compounding: $n = 5 \times 2 = 10 \text{ periods}$

3. Formula for Future Value of a Series of Payments (Annuity Formula):

The future value $FV$ of an annuity (where regular payments are made, and interest compounds periodically) is given by: $FV = PMT \times \left( \frac{(1 + i_s)^n - 1}{i_s} \right)$

Where:

• $PMT$ is the monthly deposit
• $i_s$ is the semi-annual interest rate
• $n$ is the number of periods

But since deposits are made monthly, we need to break the problem down further, considering the fact that semi-annual compounding occurs every 6 months, while payments are monthly.

The approach involves calculating the value of each $2500 deposit using a combination of the future value formula and the adjusted semi-annual compounding. Would you like to proceed with detailed step-by-step calculations of the future value?