Question

How much should you deposit at the end of each month inte an investment account that pays 6.5% compounded morithly to hwe $ 3 milion when you retite in 45 years?

Answer 1

To calculate the monthly deposit needed to reach $3 million in 45 years with a 6.5% compounded monthly interest rate, use the formula for the future value of an ordinary annuity. Convert the annual interest rate to a monthly rate, calculate the number of deposits, plug in the values into the formula, rearrange the formula to solve for Monthly Deposit, and calculate the Monthly Deposit.

Step-by-step explanation:

To calculate the amount you should deposit at the end of each month to reach $3 million in 45 years with a 6.5% monthly compounded interest rate, you can use the formula for the future value of an ordinary annuity:

Future Value = Monthly Deposit * [((1 + Monthly Interest Rate)^(Number of Deposits) - 1) / Monthly Interest Rate]

Here's the step-by-step calculation using the given values:

1. Convert the 6.5% annual interest rate to a monthly rate by dividing it by 12: 6.5% / 12 = 0.00542
2. Calculate the number of deposits by multiplying the number of years by 12 (since there are 12 months in a year): 45 * 12 = 540 deposits
3. Plug in the values into the formula: Future Value = Monthly Deposit * [((1 + 0.00542)^(540) - 1) / 0.00542]
4. Rearrange the formula to solve for Monthly Deposit: Monthly Deposit = Future Value / [((1 + 0.00542)^(540) - 1) / 0.00542]
5. Calculate the Monthly Deposit: Monthly Deposit = $3,000,000 / [((1 + 0.00542)^(540) - 1) / 0.00542]