Question

Sosa Excavating Inc. is purchasing a bulldozer. The equipment has a price of \(100,000. The manufacturer has offered a payment plan that would allow Sosa to make 10 equal annual payments of \)16,274.53, with the first payment due one year after the purchase. Instructions (a) How much total interest will Sosa pay on this payment plan? (b) Sosa could borrow $100,000 from its bank to finance the purchase at an annual rate of 9%. Should Sosa borrow from the bank or use the manufacturer’s payment plan to pay for the equipment?

Short answer

The total interest is $62,745.3, and they should borrow from the bank to pay for the bulldozer.

Step-by-step solution

Calculation of total interest

$\begin{array}{rcl}\mathrm{Total}\mathrm{Interest}& =& \mathrm{Total}\mathrm{payment}-\mathrm{Equipment}\mathrm{price}\\ & =& (16,274.53\times 10)-100,000\\ & =& \$62,745.3\end{array}$

Choosing between bank or manufacturer’s plan

$\begin{array}{rcl}\mathrm{Present}\mathrm{value}\mathrm{factor}& =& \frac{\mathrm{Equipment}\mathrm{price}}{\mathrm{Annual}\mathrm{payments}}\\ & =& \frac{100,000}{16,274.53}\\ & =& 6.14457\end{array}$

The present value of the factor of 6.14457 for 10 years shows the interest rate of 10% per the table.

They should choose to borrow from the bank as the interest rate is lower.