ACTSC371 Study Guide - Final Guide: Compound Interest
5 Oct 2018
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We see the effect as interest moves from annual compounding to quarterly compounding to daily compounding. Consider the annual return as we move from semi-annual compounding to daily compounding for a 10% rate: We can see that as we move towards continuous compounding, the expression moves toward: But we know from calculus that: lim (cid:4672)1+. (cid:2869)(cid:2868)(cid:4673) lim (cid:4672)1+(cid:4673)= lim (cid:4672)1+. (cid:2869)(cid:2868)(cid:4673) = . (cid:2869)(cid:2868) Consider the following comparison for an 8% rate: Formula for annual rate (1+. 08)1 - 1 (1+. 08/2)2 - 1 (1+. 08/12)12 - 1 (1+. 08/365)365 - 1 e. 08 - 1. We can also calculate equivalent rates for continuously compounded rates. Example: calculate the rate j4 that is equivalent to j = 9%. We equate the annual accumulation factors and solve for i. (1 + i)4 = e. 09 or i = e. 09/4 1 i = . 022755. Example 2: calculate the rate j equivalent to j2 = 10% S = p*ej *t where t is the time in years.
