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At a nominal interest rate of i convertible semi-annually, an investment of 1000 immediately and 1500 at the end of the first year will accumulate to 2000 at the end of the second year. Under the same interest rate, what is the present value of 1000 paid at the end of the fifth year?

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Answer:

The answer is "869.76"

Explanation:

Given value:

[tex]CF_0=-1000\\\\CF_1=-1500\\\\CF_2=2000\\\\CPT \ IRR =2.8342\%\\\\[/tex]

[tex]\to Nominal\ Rate =2\times ((1+2.8342 \%)^{((\frac{1}{2})-1)}[/tex]

                          [tex]=2\times ((1.28342)^{(\frac{1}{2})-1}) \\ \\=2\times ((1.28342)^{(\frac{1}{2})-1}) \\\\ = 2.81\%[/tex]

[tex]\to 1000 = P (1+ \frac{2.83}{100})^5 \\\\\to 1000 = P (1+ 0.0283)^5\\\\\to P = \frac{1000}{(1+ 0.0283)^5}\\\\[/tex]

       [tex]= \frac{1000}{1.14973878}\\\\= 869.76[/tex]

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