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


Answered 1 year ago
Answered 1 year ago
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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 PP of payment in dollars at time tt in years if interest is compounded annually


Note that BB is the future value of PP and rr is the interest rate. Since interest rate per year is 7.75%7.75\%, assign r=0.0775r=0.0775:

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

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