Final answer:
To calculate the two equal payments, the total debt must be adjusted for the missed payments and the corresponding accrued simple interest at a rate of 10%. The interest is calculated by the time-adjusted principal with respective time periods. Lastly, the total owed amount will be divided by two to find the value of each equal payment.
Step-by-step explanation:
Calculating Equal Payments with Simple Interest
The question involves determining two equal payments that are to be made to settle a debt for a purchased spectral analyzer. The original payment plan was to make payments of $10,000 two months ago and $8,000 one month from now. However, the company has only paid $6,000 two months ago and will not be able to make the upcoming payment. A new arrangement is made to settle the remaining balance, plus the seller's 10% simple interest charge, with two equal payments: the first payment 4 months from now, and the second payment 7 months from now. We assume the focal date to be 4 months from today, as indicated by the question.
To determine the equal payments, we must calculate the total debt considering the missed payment and accrued interest. The debt two months ago was $10,000 - $6,000 = $4,000. Interest will be charged on this amount for 6 months (since we are using 4 months from now as the focal date). The upcoming missed payment is $8,000 which will carry a one-month interest charge. The simple interest I for a principal P, at an interest rate r per time period, for t time periods is given by I = P*r*t. Using this formula, we'll calculate the interest on both components of the debt.
For the $4,000 debt, with a 10% annual rate (or 0.10/12 per month) for 6 months, the interest is $4,000*(0.10/12)*6. For the $8,000 upcoming debt for just one month, the interest is $8,000*(0.10/12)*1. These amounts will be added to their respective principals to get the total debt, and then combined to get the total owed amount. This owed amount will be divided equally into two payments. It’s important to note that these calculations are an approximation, as the application of a 10% simple interest rate might differ slightly depending on specific terms defined by the lender, but for a standard case, the approach detailed here would be correct.