Final answer:
The question deals with Mathematics and involves calculating the discounted amount for an invoice and determining the present value of bond payments under different discount rates. In the given invoice scenario, a 6% discount is applicable, leading to a payment of $5,294.08. For the bond, the present value is calculated for both 8% and 11% discount rates, showing the impact of changing interest rates on present value.
Step-by-step explanation:
The subject of this question is Mathematics, specifically focusing on financial mathematics like invoice settlement and discounts, as well as present value calculations for bonds and loans.
Invoice Settlement
To determine the amount paid to settle the given invoice with payment terms of 6/10, E.O.M., we note the terms mean the buyer can take a 6% discount if the invoice is paid within 10 days of the end of the month of the invoice date. Since the invoice is dated July 15, the end of the month is July 31st. Therefore, the first day to take the discount would be August 1st, and the last day would be August 10th. As the payment was made on August 7th, within the discount period, the discounted amount can be calculated:
Discount = Invoice Amount × Discount Percentage = $5,632.00 × 0.06 = $337.92
Amount paid = Invoice Amount - Discount = $5,632.00 - $337.92 = $5,294.08
Present Value of Bond Payments
To calculate the present value of a simple two-year bond with an 8% interest rate and payments of $240 in interest each year, the formula for present value is used:
Present Value = Future Payment / (1 + Discount Rate)Number of Years
When the discount rate is 8%, the present value is:
First-year interest: Present Value = $240 / (1 + 0.08)1 = $222.22
Second-year interest + principal: Present Value = ($240 + $3,000) / (1 + 0.08)2 = $2,777.78
Total present value with an 8% rate: $3,000.00
If the discount rate increases to 11%, the recalculation would result in a lower present value for each payment:
First-year interest: Present Value = $240 / (1 + 0.11)1 = $216.22
Second-year interest + principal: Present Value = ($240 + $3,000) / (1 + 0.11)2 = $2,630.63
Total present value with an 11% rate: $2,846.85