Upon retirement (in 40 years) you want to receive $10,000 each month for a period of 28 years. This money resides in an account that pays 5.9% interest. How much money must be in the account to fulfill your goal?
To calculate the required amount of money, we need to consider the monthly withdrawals over 28 years and the interest rate. Here are the steps:
Step 1: Calculate the total number of months for the retirement period.
Since each year has 12 months, the retirement period of 28 years is equivalent to 28 x 12 = 336 months.
Step 2: Calculate the total amount to be withdrawn over the retirement period.
The desired monthly withdrawal is $10,000. So, the total amount to be withdrawn over 336 months is 336 x $10,000 = $3,360,000.
Step 3: Calculate the present value of the total amount, considering the interest rate.
The formula to calculate present value is: PV = FV / (1+r)^n
Where:
PV = Present Value (the amount required)
FV = Future Value (the total amount to be withdrawn)
r = interest rate per period (monthly interest rate = annual interest rate / 12)
n = number of periods (in this case, the retirement period in months)
In our scenario, the annual interest rate is 5.9%. So, the monthly interest rate is 5.9% / 12 = 0.0049167 (approximately).
Using the formula, we can calculate the present value:
PV = $3,360,000 / (1+0.0049167)^336
Calculating the expression ^336 (raising to the power of 336):
PV ≈ $3,360,000 / 1.917887
Dividing $3,360,000 by 1.917887:
PV ≈ $1,750,403.20
Therefore, in order to fulfill your retirement goal, you would need approximately $1,750,403.20 in the account.
To calculate how much money must be in the account to fulfill your goal, we can use the concept of present value. Present value is the current worth of a future sum of money, considering the time value of money.
In this case, you want to receive $10,000 each month for a period of 28 years, starting 40 years from now. The interest rate is 5.9%.
To calculate the present value of this future stream of cash flows, we can use the present value of an annuity formula:
PV = A * [(1 - (1 + r)^(-n)) / r]
Where PV is the present value, A is the monthly payment, r is the interest rate per month (expressed as a decimal), and n is the number of months.
Let's plug in the values provided:
A = $10,000
r = 5.9% / 12 = 0.059/12 = 0.004917 (monthly interest rate)
n = 28 * 12 = 336 (number of months)
PV = $10,000 * [(1 - (1 + 0.004917)^(-336)) / 0.004917]
Calculating this formula will give us the amount of money that must be in the account to fulfill your goal.