Question

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

Answer 1

The value of X is 2455.77

Step-by-step 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×
`(1)/((1 + 0.08)^(4) )` + 5000×
`(1)/((1 + 0.08)^(6) )` = X×
`(1)/((1 + 0.08)^(2) )` + 1000×
`(1)/((1 + 0.08)^(3) )` + 2X×
`(1)/((1 + 0.08)^(9) )`

2,205.089 + 3,150.84 = 793.83 + X(
`(1)/((1 + 0.08)^(2) )` +
`(1)/((1 + 0.08)^(9) )` )

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