Answer:
$797,837
Explanation:
the first withdrawal is $50,000
the second is $51,500
and so on...
the formula that used to solve the interest rate earned by the annuity is:
$50,000 x {[(1 + i)³⁰ - (1 + 3%)³⁰] / [(1 + i)³⁰ x (i - 3%)]} x (1 + i) = $5,000 x {[(1 + i)³⁰ - (1 + 3%)³⁰] / (i - 3%)}
we start to simplify the equation by cancelling {[(1 + i)³⁰ - (1 + 3%)³⁰] / (i - 3%)}
[$50,000 x (1 + i)] / (1 + i)³⁰ = $5,000
now we cancel $5,000 on each side:
[10 x (1 + i)] / (1 + i)³⁰ = 1
now lets take away (1 + i):
10 / (1 + i)²⁹ = 1
things get a little bit more simple now:
10 = (1 + i)²⁹
²⁹√10 = ²⁹√(1 + i)²⁹
1.082636734 = 1 + i
i = 1.082636734 - 1 = 0.082636734 = 8.2636734%
now we replace i in any equation:
= $50,000 x {[(1 + 0.082636734)³⁰ - 1.03³⁰] / [(1 + 0.082636734)³⁰ x (0.082636734 - 0.03)]} x (1 + 0.082636734)
= $50,000 x {[10.82636738 - 2.427262471] / [10.82636738 x 0.052636734]} x (1 + 0.082636734)
= $50,000 x {8.399104909 / 0.56986462} x (1.082636734)
= $50,000 x 14.73877236 x 1.082636734
= $797,837
= New Forecast
= Previous period's forecast.
= Smoothing Constant
= Previous period's Actual Demand.