Question

You are planning to make monthly deposits of $380 into a retirement account that pays 10 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your retirement account be in 30 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

To calculate the future value of your retirement account after 30 years, considering monthly deposits and compounding interest, you can use the formula for the future value of an ordinary annuity:

Step-by-step explanation:

Retirement Account Future Value

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

Where:

FV = Future value of the retirement account

P = Monthly deposit amount ($380)

r = Monthly interest rate (10% / 12 = 0.0083333)

n = Number of periods (30 years * 12 months = 360)

Now we can substitute the values into the formula:

FV = 380 * ((1 + 0.0083333)^360 - 1) / 0.0083333

Calculating this expression, we find:

FV ≈ $1,641,443.91

Therefore, your retirement account will be approximately $1,641,443.91 in 30 years.