A $2000 loan is to be repaid with payments of $1200 in 1 year,$800 in 4 years,and $400 in n years,assuming a nominal interest rate of 6% compounded annually.Determine n.

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Quizplus · Accepted Answer

The present value of the loan must equal the present value of the payments. Using the formula for present value, $PV = \frac{P}{(1+i)^n}$, where $PV$ is the present value, $P$ is the payment, $i$ is the interest rate, and $n$ is the number of years, we can set up the equation:$$2000 = \frac{1200}{(1+0.06)^1} + \frac{800}{(1+0.06)^4} + \frac{400}{(1+0.06)^n}$$Solving for $n$, we find that $n = 9.18$ years.

A $2000 Loan Is to Be Repaid with Payments of $1200