Answer:
The future worth of the retirement is $831,514.26
Explanation:
Future worth of a geometric gradient series is required
First Cash flow (A1) = $19,000 ($190,000 * 10%)
Gradient (g) = 0.04
Interest rate = 6% per year
Length of series = 16
We first calculate the Present worth of the series by using geometric gradient series present worth factor as follows
P = A1[ 1-(1+g)^n*(1+i)^-n / i - g]
= 19,000 [ 1 - (1 + 0.04)^13 * (1 + 0.06)^-16 ] / 0.06 - 0.04
= [19,000 - 19,000 * (1 + 0.04)^13 * (1 + 0.06)^-16] / 0.06 - 0.04
= [19,000 - 19,000(1.66507 * 0.393647)] / 0.02
= [19,000 - 19,000(0.65545)] / 0.02
= [19,000 - 12453.55] /0.02
= 6546.45 / 0.02
= 327,322.50
Now, we calculate the future worth of the series
F= P(F/P, i, n)
F= 327,322.50 (F/P 6%, 16)
F = 327,322.50 / 2.5404
F = $831,514.26
Therefore, the future worth of the retirement is $831,514.26
