Final answer:
To determine the necessary monthly deposit to reach a $2,000,000 retirement goal with an initial investment of $5000 at an 11.6% interest rate, utilize the future value of an annuity formula and subtract the future value of the initial investment, which grows at the same rate, from the target amount.
Step-by-step explanation:
You're asking how much you would need to make monthly deposits at the beginning of the month, with an initial investment of $5000 and an interest rate of 11.6%, to retire with $2,000,000 in 35 years. To solve this, we need to use the future value of an annuity formula, which is FV = P * [ ((1 + r)^n - 1) / r ], where FV is the future value, P is the deposit, r is the monthly interest rate, and n is the total number of deposits.
First, we convert the annual interest rate to a monthly rate by dividing it by 12, which gives us 0.0967. We'll be making 35 * 12 = 420 deposits.
Next, we must subtract the future value of the $5000 initial investment from the desired $2,000,000 retirement goal. Assuming this $5000 also grows at a rate of 11.6%, compounded monthly for 35 years.
The future value of $5000 is calculated using the compound interest formula: FV = PV * (1 + r)^n, where PV is the present value. So the future value of the initial $5000 is $5000 * (1 + 0.0967)^420. Assuming this amount doesn't equal $2,000,000, we would then solve for P in the annuity formula to find out the necessary monthly deposit.
The exact amount can be found using financial calculators or spreadsheet software, as the resulting equation after inserting all the values will be complex and not easily solvable without computational help. This process highlights the power of compound interest and the importance of regular savings for retirement planning.