MAT133Y1 Lecture Notes - Lecture 3: Compound Interest
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MAT133Y1 Full Course Notes
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Mat133y1y - lecture 3 - chapter 5. 3: continuous compounding (continued),chapter 5. 4: If interest is at nominal annual rate r, compounded continuously, a principal will grow to ert in t years. In half a year, will grow to pe0. 07 x 0. 5 = pe0. 035: in half a year, money grows by the ratio e0. 035. Effective interest over half a year is e0. 035-1. Equivalent rates = having the same effective rate over any given time interval . So if interest is compounded semi-annually to give e0. 035-1 as effective semiannual rate, then: r/n = e0. 035-1. (r = nominal annual rate). Let t years be the time for money to triple. 3 = e0. 05 ln 3 = e0. 05 x ln(e) ln3/0. 05 = t or t = 20ln3 t = 21. 972 or 22 years. So if x cannot equal 1, the sum of the series is: 1+ x + + xn-1 = xn-1 / x-1.
