# 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.