You want to save $200 a month for the next 24 years and hope to earn an average rate of return of 11 percent. How much more will you have at the end of the 24 years if you invest your money at the beginning of each month rather than the end of each month?
2,238.87
To calculate how much more you will have at the end of 24 years if you invest your money at the beginning of each month rather than the end of each month, you can use the concept of the time value of money, specifically the concept of compounding interest. Here are the steps to calculate it:
Step 1: Calculate the future value of monthly deposits made at the beginning of each month.
To do this, you can use the formula for the future value of an ordinary annuity:
Future Value = P * (1 + r)^n - 1 / r
Where:
P = monthly deposit amount = $200
r = monthly interest rate = (1 + annual interest rate)^(1/12) - 1
n = number of periods = 24 years * 12 months/year = 288
Step 2: Calculate the future value of monthly deposits made at the end of each month.
Using the same formula, you can calculate the future value of deposits made at the end of each month. The only difference is that the number of periods remains the same.
Step 3: Calculate the difference in the future values.
Subtract the future value of deposits made at the end of each month (from step 2) from the future value of deposits made at the beginning of each month (from step 1).
This difference represents how much more you would have at the end of the 24 years if you invest your money at the beginning of each month rather than the end of each month.
Note: It is important to assume that the monthly deposits are made consistently and without interruption.
I will calculate the specific values for you now.