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# You are considering whether to buy or lease a machine whose purchase price is $\ 12,000$. Taxes on the machine will be $\ 580$ due in one year, $\ 464$ due in two years, and $\ 290$ due in three years. If you buy the machine, you expect to be able to sell it after three years for $\ 5,000$. If you lease the machine for three years, you make an initial payment of $\ 2650$ and then three payments of $\ 2650$ at the end of each of the next three years. The leasing company will pay the taxes. The interest rate is $7.75 \%$ per year, compounded annually. Should you buy or lease the machine? Explain.

Solution

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The goal of this task is to determine if it is better to lease or buy the machine. Determine total present value of the payments for leasing the machine. Use formula of present value $P$ of payment in dollars at time $t$ in years if interest is compounded annually

$P=\dfrac{B}{(1+r)^t}.$

Note that $B$ is the future value of $P$ and $r$ is the interest rate. Since interest rate per year is $7.75\%$, assign $r=0.0775$:

\begin{aligned} P&=\dfrac{B}{(1+0.0775)^t}\\ &=\dfrac{B}{(1.0775)^t}. \end{aligned}

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