Question

you would like to be able to withdraw $10,000 per month for the 30 years you are in retirement. how much do you need to save each month for the 40 years you are working? assume the interest rate is 7% per year and that you begin saving one month from today and make your first withdraw one month after you retire.

Answer 1

To calculate how much you need to save each month for the 40 years you are working to withdraw $10,000 per month for the 30 years you are in retirement, you would need to save approximately $11,765.54 each month.

Step-by-step explanation:

To calculate how much you need to save each month for the 40 years you are working, you can use the concept of the present value of an annuity. Given that you want to withdraw $10,000 per month for the 30 years you are in retirement and the interest rate is 7% per year, you can use the formula: PMT = PV × (r/(1-(1+r)^(-n)))

Where PMT is the monthly savings, PV is the desired retirement income, r is the interest rate per period, and n is the number of periods. Plugging in the given values, we have:

PMT = $10,000 × (0.07/(1-(1+0.07)^(-30)))

PMT = $10,000 × (0.07/0.633)

PMT ≈ $11,765.54

So, you would need to save approximately $11,765.54 each month for the 40 years you are working to be able to withdraw $10,000 per month for the 30 years you are in retirement.

Answer 2

To determine how much to save each month for retirement, apply the future value of an annuity formula for the withdrawal period, and then use the present value of an annuity formula for the accumulation period, considering a 7% annual interest rate.

Step-by-step explanation:

Calculating how much to save each month for retirement involves understanding the concept of compound interest and applying it to retirement savings and withdrawal plans. In the scenario presented, one needs to save for 40 years at an interest rate of 7% annually to be able to withdraw $10,000 per month for 30 years after retirement.

To solve this problem, we would use the future value of an annuity formula for the retirement phase to calculate the total needed at the beginning of retirement, and then use the present value of an annuity formula for the saving phase to find how much to save each month during the 40 years of work. The example of saving $3,000 early in life and letting it grow at 7% per year to become $44,923 after 40 years demonstrates the power of compound interest.

Economists recommend saving around 15% of income for retirement, which is also an important factor to consider when determining how much to save monthly.