A civil engineer planning for her retirement places 10% of her salary each year into a high-technology stock fund. If her salary this year (end of year 1) is $190,000 and she expects her salary to increase by 4% each year, what will be the future worth of her retirement fund after 16 years provided it earns 6% per year

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

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