You borrows $10,000 today at j₂ = 8%.You pay back $7000 at the end of 2-years and another $7000 at the end of n-years (from today).What is the value of n? (years,days)

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Quizplus · Accepted Answer

The problem can be solved using the concept of the time value of money, specifically the present value (PV) formula. The total present value of the loan must equal the sum of the present values of the two payments. Given an 8% annual interest rate, compounded semi-annually, we calculate the present value of each payment and solve for $n$.The present value of the first payment of $7000 due in 2 years is calculated as:$$PV_1 = \frac{7000}{(1 + \frac{0.08}{2})^{2*2}}$$The present value of the second payment of $7000 due in $n$ years is:$$PV_2 = \frac{7000}{(1 + \frac{0.08}{2})^{2n}}$$The sum of these present values equals the initial loan amount of $10,000:$$PV_1 + PV_2 = 10,000$$Solving this equation for $n$ gives us the duration in years. When you do the math, you find that $n$ equals approximately 7 years and 30 days, making option A the correct answer.

You Borrows $10,000 Today at J2 = 8

You Borrows $10,000 Today at J₂ = 8