“Compound Interest”的概念、定义、习题解题方法及翻译-数学辞典

单词

Compound Interest

释义

Compound Interest

Let be the Principal (initial investment), be the annual compounded rate, the ``nominal rate,'' be the number of times Interest is compounded per year (i.e., the year is divided into ConversionPeriods), and be the number of years (the ``term''). The Interest rate per ConversionPeriod is then

(1)

If interest is compounded

times at an annual rate of

(where, for example, 10% corresponds to

), then theeffective rate over

the time (what an investor would earn if he did not redeposit his interest after each compounding)is

(2)

The total amount of holdings

after a time

when interest is re-invested is then

(3)

Note that even if interest is compounded continuously, the return is still finite since

(4)

where e is the base of the Natural Logarithm.

The time required for a given Principal to double (assuming Conversion Period) is given by solving

(5)

(6)

where Ln is the Natural Logarithm. This function can be approximated by the so-called Rule of 72:

(7)

See also e, Interest, Ln, Natural Logarithm, Principal, Rule of 72, Simple Interest

References

Kellison, S. G. The Theory of Interest, 2nd ed. Burr Ridge, IL: Richard D. Irwin, pp. 14-16, 1991.

Milanfar, P. ``A Persian Folk Method of Figuring Interest.'' Math. Mag. 69, 376, 1996.

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