Answered

Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Get quick and reliable solutions to your questions from a community of experienced professionals on our platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

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

Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.