Earl Watkins is ready to retire and has saved up $250,000 for that purpose. He places all of this money into an account which will pay him annual payments for 20 years. How large will these annual payments be if the account earns 17% compounded annually?
payment -- P
P( 1 - 1.17^-20)/.17 = 250000
I get P = $44,422.59
To determine the size of the annual payments Earl will receive, we need to use the formula for the future value of an ordinary annuity.
The formula is:
FV = Pv * [(1 + r)^n - 1] / r,
Where:
FV represents the future value,
Pv is the present value (initial investment),
r is the interest rate per compounding period,
n is the number of compounding periods.
In this case, Earl's present value is $250,000, the interest rate is 17% per year, and he will receive payments for 20 years.
First, let's convert the interest rate to a decimal by dividing it by 100: 17% / 100 = 0.17.
Next, let's substitute the values into the formula:
FV = 250,000 * [(1 + 0.17)^20 - 1] / 0.17.
Now, let's simplify the formula:
FV = 250,000 * [1.17^20 - 1] / 0.17,
FV = 250,000 * [1.71699 - 1] / 0.17,
FV = 250,000 * 0.71699 / 0.17.
Calculating the expression gives us:
FV = 250,000 * 4.21817,
FV = $1,054,542.
Therefore, the size of the annual payments Earl will receive from his account will be approximately $1,054,542.