You want to accumulate $1,000,000 in retirement funds by your 65th birthday. Today is your 30th birthday, and you plan on making annual investments into a mutual fund that you project will earn a 10% annual rate of return. Your first deposit will take place today and your last deposit will take place on your 65th birthday. What is the amount of the annual payment you must make each year in order to have $1,000,000 in your account on the day you make your last deposit - that is, on your 65th birthday?
2927.49
To calculate the amount of the annual payment you must make in order to have $1,000,000 in your account on your 65th birthday, you can use the future value of an ordinary annuity formula.
The formula for the future value of an ordinary annuity is:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = Future value of the annuity
P = Annual payment
r = Annual interest rate
n = Number of periods
In this case, the future value (FV) is $1,000,000, the annual interest rate (r) is 10% (0.10), and the number of periods (n) is the difference between your 65th birthday age and your current age (65 - 30 = 35).
Substituting the values into the formula, we get:
$1,000,000 = P * ((1 + 0.10)^35 - 1) / 0.10
To solve for P, we can first simplify the expression by calculating ((1 + 0.10)^35 - 1) / 0.10, which is approximately equal to 13.783.
So the equation becomes:
$1,000,000 = P * 13.783
To isolate P, the annual payment, we divide both sides of the equation by 13.783:
P = $1,000,000 / 13.783
Calculating this, we find that the annual payment you must make each year to accumulate $1,000,000 by your 65th birthday is approximately $72,520.56.