Question 5.1: A savings bank is selling long-term savings certificates tha......

Schaum’s Outline of Engineering Economics [1215911]

A savings bank is selling long-term savings certificates that pay interest at the rate of 7 $\frac{1}{2}$ % per year, compounded continuously. The bank claims that the actual annual yield of these certificates is 7.79%. What does this mean?

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The nominal interest rate is 7 $\frac{1}{2}$ %. Since the interest is compounded continuously, the effective annual interest rate is given by (5.1) as

$i = \underset{m→∞}{\lim}\left[\left(1 + \frac{r}{m}\right)^m – 1\right] = e^r – 1$ (5.1)

i = e $^{0.075}$ – 1 = 0.077884 ≈ 7.79%

Formula (5.1) is very convenient, provided a calculator is available to carry out the exponentiation. Tabulated values of the effective annual interest rate may be used instead; see Appendix B.

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