A student borrows $2,000 today and they agree to pay off the loan with one payment of $2,590.06 to be made at the end of 3 years time.It is then agreed that,instead of paying off the loan with one payment,the student can pay off the loan with a payment of $1000 one year from now and $X two years from now.Given that j₂ = 6%,determine $X. A)$1190.12 B)$1286.20 C)$1380.48 D)$1529.16

Question

Quizplus · Accepted Answer

Using the formula for future value of a single sum:
$2,000*(1+0.06)^3 = $2,390.20
The amount owed after 3 years is $2,390.20.
To calculate $X, we need to subtract the $1000 payment made in 1 year from the amount owed and then discount it back 2 years at 6%:
($2,390.20 - $1,000) / (1+0.06)^2 = $1,380.48
Therefore, the value of X is $1,380.48.

A Student Borrows $2,000 Today and They Agree to Pay