Question 5.6: At what rate must funds be continuously added to a savings a......

Schaum’s Outline of Engineering Economics [1215911]

At what rate must funds be continuously added to a savings account in order to accumulate $10 000 in 15 years, if interest is paid at 5% per year, compounded continuously?

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By (5.10),

$\bar{A}/F = \frac{r}{e^m – 1} (5.10) \\\\ \bar{A} = \$10 000\frac{0.05}{e^{(0.05)(15)} – 1} = \$447.63$ per year

that is, $447.63 must flow uniformly into the account each year.

It is interesting to compare this result to a series of uniform, end-of-year payments, with interest compounded continuously as above. The amount of each such payment is given by (5.5) as

A/F  =  \frac{e^r  –  1}{e^m  –  1}    (5.5)

A = $10 000[A/F, 5%, 15] = $10 000(0.0459) = $459 per year

Thus, an additional $11.37 would be required each year if the payments were made annually rather than continuously.

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