Q1. $1,000 is invested for 20 years. For years 1-5, the investment rate is i (2)

Question

Q1. $1,000 is invested for 20 years. For years 1-5, the investment rate is i(2) =11%. For years 6-10, the investment rate is = 6% . For years 11-15, the investment rate is d(4) =14% . For years 16-20, the investment rate is i = 8% . Find the accumulated value of the investment at the end of the 20 years.

Q2. Let d(2) be the nominal annual rate of discount convertible semiannually at which you can double your money in 8 years. Find i(4) , the equivalent nominal annual rate of interest convertible quarterly.

Explanation / Answer

1)

value of investment at end of year 20 =$ 6379.51 (approx)

2) (1+ i^4 /4)^-4 = (1-d^2/2)^2

= 1- d^2 /2 = (1+i^4 /4)^-2

=d^2 = [1-(1-i^4 /4)^-2 ]

year Investment rate value of investment 1 11 1110     [1000(1+.11)] 2 11 1232.1 3 11 1367.63 4 11 1518.07 5 11 1685.06 6 6 1786.16 7 6 1893.33 8 6 2006.93 9 6 2127.35 10 6 2254.99 11 14 2570.69 12 14 2930.59 13 14 3340.87 14 14 3808.59 15 14 4341.79 16 8 4689.13 17 8 5064.26 18 8 5469.41 19 8 5906.96 20 8 6379.51

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