You borrow $2000 today.The loan is due in 3 years,with interest at j₁ = 9%.It is agreed that you will instead pay $1000 one year from now and $X two years from now.If money is worth j₂ = 6%,what is the value of X?

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Quizplus · Accepted Answer

To find the value of X, we need to calculate the present value of the payments and equate it to the loan amount. The present value of $1000 paid in one year at 6% interest is $1000 / (1 + 0.06) = $943.40. The present value of $X paid in two years at 6% interest is $X / (1 + 0.06)^2. The present value of the total loan amount of $2000 at 9% interest for 3 years is $2000 / (1 + 0.09)^3 = $1547.98. Setting the present values equal gives $943.40 + $X / (1.1236) = $1547.98. Solving for X gives X = $1380.48.

You Borrow $2000 Today