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Luis has an obligation to pay a sum of $3,000 in four years from now and a sum of $5,000 in six years from now. His creditor permits him to discharge these debts by paying $X in two years from now, $1000 in three years from now, and a final payment of $2X in nine years from now. Assuming an annual effective rate of interest of 8%, find X

Sagot :

nuhulawal20

Answer:

The value of X is 2455.77

Explanation:

Given the data in the question;

annual effective rate of interest of 8%, = 0.08

Now, we discount all the ash flows to present value, so we get;

3000×[tex]\frac{1}{(1 + 0.08)^{4} }[/tex] + 5000×[tex]\frac{1}{(1 + 0.08)^{6} }[/tex]  = X×[tex]\frac{1}{(1 + 0.08)^{2} }[/tex] + 1000×[tex]\frac{1}{(1 + 0.08)^{3} }[/tex] + 2X×[tex]\frac{1}{(1 + 0.08)^{9} }[/tex]  

2,205.089 + 3,150.84 = 793.83 + X( [tex]\frac{1}{(1 + 0.08)^{2} }[/tex] + [tex]\frac{1}{(1 + 0.08)^{9} }[/tex] )

5355.929 - 793.83 = X( 0.8573 + 1.0004 )

4,562.099 = X( 1.8577 )

X = 4,562.099 / 1.8577

X = 2455.77

Therefore; value of X is 2455.77

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