Dello, i need help with this problem.
Find the periodic withdrawals PMT for the annuity given. HINT [See Example 4.] (Assume end-of-period withdrawals and compounding at the same intervals as withdrawals. Round your answer to the nearest cent.)
$100,000 at 6%, paid out monthly for 17 years
To find the periodic withdrawals PMT for the annuity, we can use the present value of an annuity formula.
The formula for calculating the present value of an annuity is:
PMT = PV / ((1 - (1 + r)^(-n)) / r)
Where:
PMT = periodic withdrawal amount
PV = present value (initial amount)
r = periodic interest rate
n = number of periods
In this case, the present value (PV) is $100,000, the interest rate (r) is 6%, and the number of periods (n) is 17 years multiplied by 12 months per year, which equals 204 months.
Let's plug in these values into the formula:
PMT = 100000 / ((1 - (1 + 0.06)^(-204)) / 0.06)
Now let's simplify the equation and calculate the result:
PMT = 100000 / ((1 - 0.143854) / 0.06)
= 100000 / (0.856146 / 0.06)
= 100000 / 14.2691
≈ $7,004.42
Therefore, the periodic withdrawal amount (PMT) for the annuity is approximately $7,004.42, rounded to the nearest cent.