John is a 45 year old and wants to retire at age 65. He wishes to make monthly deposit into an account paying 9% compounded monthly so when he retires he can withdraw $320 a month for 30 years. How much should John deposit each month?
solve for x
x(1.0075^240 - 1)/.0075 = 320(1 - 1.0075^-360)/.0075
the denominators will cancel, so
x = 320*(1 - 1.0075^-360)/(1.0075^240 - 1)
= ...
you do the button pushing.
Let me know what you get
To calculate the monthly deposit John should make, we can use the concept of present value. The present value is the current value of a future sum of money, taking into account the time value of money.
In this case, we need to find the present value of the monthly withdrawal of $320 for 30 years, considering the interest rate of 9% compounded monthly.
Here's how you can calculate the monthly deposit that John should make:
1. Determine the total number of months: Since John wants to retire at age 65 and withdraw $320 a month for 30 years, we need to calculate the total number of months.
Total Months = 30 years * 12 months/year = 360 months
2. Calculate the present value of the monthly withdrawal: The present value formula for a series of future cash flows is:
PV = CF * (1 - (1 + r)^(-n)) / r
PV: Present Value of the monthly withdrawal
CF: Cash Flow (monthly withdrawal of $320)
r: Interest Rate per Period (9% / 12 months = 0.75% or 0.0075 in decimal form)
n: Number of Periods (360 months)
PV = $320 * (1 - (1 + 0.0075)^(-360)) / 0.0075
3. Calculate the monthly deposit:
The monthly deposit can be calculated using the present value formula by rearranging the formula to solve it for CF:
CF = PV * r / (1 - (1 + r)^(-n))
Monthly Deposit = PV * r / (1 - (1 + r)^(-n))
Now let's calculate the monthly deposit using the above formula:
PV = $320 * (1 - (1 + 0.0075)^(-360)) / 0.0075
≈ $32,559.94
Monthly Deposit = $32,559.94 * 0.0075 / (1 - (1 + 0.0075)^(-360))
≈ $168.71
Therefore, John should deposit approximately $168.71 each month into the account to be able to withdraw $320 per month for 30 years, assuming a 9% interest rate compounded monthly.