## Related questions with answers

A recently graduated mechanical engineer wants to build a reserve fund as a safety net to pay his expenses in the unlikely event that an unexpected emergency arises. His aim is to have $45,000 developed over the next 3 years, with the proviso that the amount must have the same purchasing power as$45,000 today. If the expected market rate on investments is 8% per year and inflation is averaging 2% per year, find the annual amount necessary to meet his goal.

Solution

VerifiedThe future worth (inflation rate = 2% and n = 3 years):

$\begin{align*} \text{FW}&=45{,}000(F/P, 2\%, 3)\\[7pt] &=45{,}000(1.0612)\\[7pt] &= \boxed{\$47{,}754}\\ \end{align*}$

The annual worth in future dollars ($i_f$ = 8%):

$\begin{align*} \text{AW}&=47{,}754(A/F, 8\%, 3)\\[7pt] &=47{,}754(0.30803)\\[7pt] &= \boxed{\$14{,}710}\\ \end{align*}$

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