To find the future value of your investment, we'll use the formula for the future value of a series of cash flows, which includes both the initial investment and the regular monthly contributions.

1. Initial Investment: $30,000
2. Monthly Contribution: $2,000
3. Annual Interest Rate: 10% (or 0.10)
4. Number of Years: 18 years
5. Total Number of Months: 18 years × 12 months/year = 216 months

Now, we will use the formula for the future value (FV) of a series of cash flows, which is typically:

[ FV = P \times (1 + r)^n + PMT \times \frac{((1 + r)^n - 1)}{r} ]

Where:

• ( P ) is the initial principal (initial investment)
• ( PMT ) is the monthly contribution
• ( r ) is the monthly interest rate (annual rate divided by 12)
• ( n ) is the total number of contributions (number of months)

Calculating:

1. Convert annual interest rate to monthly:

   • ( r = \frac{0.10}{12} = 0.008333 )

2. Total number of months:

   • ( n = 216 )

Now substitute the values into the formula:

Future Value of Initial Investment:

[ FV_{initial} = 30000 \times (1 + 0.008333)^{216} ]

Future Value of Monthly Contributions:

[ FV_{contributions} = 2000 \times \frac{(1 + 0.008333)^{216} - 1}{0.008333} ]

Final Calculation:

After performing the calculations:

• ( FV_{initial} \approx 30000 \times 6.350 \approx 190,500 )
• ( FV_{contributions} \approx 2000 \times 233.254 \approx 466,508 )

Total Future Value:

[ Total , FV \approx 190,500 + 466,508 \approx 657,008 ]

Thus, after 18 years with the given investment strategy, you would have approximately $657,008.