Given the following table of interest rates Investment Year RatesPortfolio Rates

Question

Given the following table of interest rates Investment Year RatesPortfolio Rates (in %) (in %) Calendar Year of Investment y Calendar Year of Portfolio Rates +4 2000 4.2 4.7 5.2 4.74.5 2004 2001 4.5 4.9 4.8 5.14.8 2005 2002 4.7 5 5.4 5 5.1 2006 2003 5.3 5 4.8 5 5.6 2007 2004 5.9 6.3 6.6 5.5 2005 6 5.7 5.6 6.7 4.4 6.8 2006 2007 Olivia deposits 1000 on January 1, 2004. Find the accumulated value of her investment on December 31, 2006 Using the investment year method: AV- Using the portfolio yield method: AV =

Explanation / Answer

In the above question the investment period in portfolio is 3 years (1Jan 2004 - 31 Dec 2006)

Calculation of Accumulated value of Investment using Investment yield Method -

Since we invested $1000 at the beginning of 2004, 2005 and 2006, we find the balance of each contribution over the specified intervals of time and sum them together. So, denoting CyCy to be the year in which our contribution was made, we obtain:

C2004 = 1000(1.059) (1.063) (1.066) (1.055) = 1266.015

C2005 = 1000(1.06) (1.057) (1.056) = 1183.16

C2006 = 1000(1.067) (1.044) = 1113.95

(1266.015+1183.16+1113.95) = 3563.125

Accumulated Value of Investment under Investment Year Method = 3563.125

Calculation of Accumulated value of Investment using Portfolio Yield Method -

Initial Deposit by Olivia - $1000 (considered to be X)

Portfolio rates (2004 (R1) = 4.5, (2005 (R2) = 4.8, (2006 (R3) = 5.1

Accumulated Value = (1000*104.5/100) = 1045

                                      (1045*104.8/100) = 1095.16

                                      (1095.16*105.1/100) = 1151.01316

Accumulated value at the end of December 2016 using portfolio yield method is = 1151.01316

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