Question

suppose you want to have $400,000 for retirement in 20 years. your account earns 5% interest. a) how much would you need to deposit in the account each month

Answer 1

To calculate the amount needed to be deposited each month for a retirement fund, use the formula for the future value of an ordinary annuity. Plugging in the given values, you would need to deposit approximately $782.92 each month into the account.

Step-by-step explanation:

To calculate the amount needed to be deposited each month, we 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 ($400,000)
• P is the deposit amount each month
• r is the interest rate per period (5% divided by 12, since it's monthly)
• n is the number of periods (20 years multiplied by 12 months)

Plugging in the given values:

400,000 = P × [(1 + (0.05/12))^(20 * 12) - 1] / (0.05/12)

Solving for P, we get:

P = 400,000 / [(1 + 0.0041667)^(240) - 1] / 0.0041667

Therefore, you would need to deposit approximately $782.92 each month into the account.