Question

The Apex Company sold a water softener to Marty Smith. The price of the unit was $350. Marty asked for a deferred payment plan, and a contract was written. Under the contract, the buyer could delay paying for the water softener if he purchased the coarse salt for recharging the softener from Apex. At the end of 2 years, the buyer was to pay for the unit in a lump sum, with interest at a quarterly rate of 1.5%. According to the contract, if the customer ceased buying salt from Apex at any time prior to 2 years, the full payment due at the end of 2 years would automatically become due. Six months later, Marty decided to buy salt elsewhere and stopped buying from Apex, whereupon Apex asked for the full payment that was to have been due 18 months hence. Marty was unhappy about this, so Apex offered as an alternative to accept the $350 with interest at 10% per semiannual period for the 6 months. Which alternative should Marty accept? Explain.

Answer 1

The student's question involves a mathematical decision about which payment option is more financially favorable for Marty Smith regarding a water softener purchase, where the assessment requires an understanding of different interest rate structures. Marty must choose between paying with the original quarterly interest rate or a new 10% semiannual rate, based on the accumulated total.

Step-by-step explanation:

The subject of this question is a real-life application of Mathematics, specifically in assessing which financial option is more favorable for a buyer who has stopped purchasing salt from the seller. Marty Smith must decide between two alternatives for paying for a water softener from Apex Company. The original agreement was for deferred payment with interest at a quarterly rate of 1.5%, but since Marty chose to discontinue buying salt from Apex, he must pay earlier than the agreed 2-year period.

To calculate the better option for Marty, we would need to compute the total amount payable under both the original contract terms and the new 10% semiannual interest rate for 6 months. However, without explicit financial formulas or more detailed information, we cannot complete the computations in this answer. Generally speaking, Marty should accept the alternative with the lower total payment amount.

Important to note is the concept of commercial water softeners used in this scenario, as they treat hard water, and the need for coarse salt for their proper functioning. Additionally, the calculation involves understanding the effects of interest rates on deferred payments.