# Total Cost Comparison: Buying vs Leasing Equipment

## What are the two options Natasha has for acquiring special equipment for her job?

Natasha needs special equipment for her job as a builder. She has two options. She can buy the equipment which costs $12 800. Natasha will finance this purchase through the vendor by making regular monthly payments over 6 years at an interest rate of 7.3%, compounded monthly. At the end of the 6 years, the equipment will be worthless. She can also lease the equipment at a cost of $185 per month. Both options require a down payment of $1980.

## Final Answer

This problem involves finance in mathematics where we compare the total costs of two options: buying equipment with interest or leasing it. Firstly, we need to calculate the monthly repayments for the buying option considering the interest rate and then sum it all. Secondly, we calculate the total leasing cost. Finally, we compare which option is cheaper.

## Explanation

The subject of the question is Mathematics and it's related to finance and decision making. Natasha needs to compare the total cost of purchasing the equipment with the cost of leasing it over the same period. To calculate the total cost of purchasing the equipment, we need to consider both the initial purchase price and the interest that will accrue over the 6 years. If the interest rate is 7.3% per annum and compounded monthly, the monthly interest rate would be 7.3% ÷ 12. The monthly repayment can be calculated using the formula for compound interest. After the calculation, the total cost of buying would be the sum of all these monthly repayments. On the other hand, the total cost of leasing the equipment would be $185 per month multiplied by 12 months per year times 6 years. Finally, we compare the two total costs to find out which option is less expensive.