How much money should be deposited each year for 30 years at 3% to accumulate $1000,000?

I find that an EXCEL spreadsheet is very helpful for these kinds of problems.

If one deposits an amount P, growing for 30 years, the amount will grow to P*(1.03)^30. You want to solve for P such that:
P*1.03^30 + P*1.03^29 + ... P*1.03^1 = 1,000,000. Factor out the P, use EXCEL to calculate the sumation series, divide the 1M by the sumation and tada, you have your answer.

To determine how much money should be deposited each year for 30 years at a 3% interest rate to accumulate $1,000,000, you can use the formula for the future value of an ordinary annuity:

FV = P * (1 + r)^n - 1 / r

Where:
FV is the future value of the annuity ($1,000,000)
P is the amount to be deposited each year (unknown)
r is the interest rate per period (3% or 0.03)
n is the number of periods (30 years)

Rearranging the formula to solve for P gives:

P = FV * r / ((1 + r)^n - 1)

Substituting the given values, we have:

P = $1,000,000 * 0.03 / ((1 + 0.03)^30 - 1)

Using EXCEL or any other numerical software, you can calculate the expression inside the brackets [(1 + 0.03)^30 - 1] to get the result:

P = $1,000,000 * 0.03 / (1.972093 - 1)

P = $30,000 / 0.972093

P ≈ $30,829.75

Therefore, approximately $30,829.75 should be deposited each year for 30 years at a 3% interest rate to accumulate $1,000,000.