Pergunta

3- curfa empresa desconta em um bonco thas depilicatas numa data a taxa de dercon to comerical imples de 6 % a.m conforme a tabela abaixo. 20 debrmine o valor atual resabido pela empresa.
Solução

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ManuelMestre · Tutor por 5 anos
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### O valor atual recebido pela empresa é R$36,000.00.
Explicação
## Step 1: Understand the Problem<br />### The problem involves calculating the present value of three duplicates (financial instruments) that are discounted at a simple commercial discount rate of \(6\%\) per month. We need to determine the total amount received by the company after discounting these duplicates.<br /><br />## Step 2: Identify the Formula for Simple Commercial Discount<br />### The formula for calculating the present value using simple commercial discount is:<br />\[ PV = FV \times (1 - d \times t) \]<br />where \(PV\) is the present value, \(FV\) is the future value or nominal value, \(d\) is the discount rate per period, and \(t\) is the time in periods until maturity.<br /><br />## Step 3: Apply the Formula to Each Duplicate<br />### For each duplicate, we will calculate the present value using the given nominal values, the discount rate of \(6\%\) per month, and their respective maturity periods.<br /><br />### **Duplicate 1:**<br />- Nominal Value (\(FV\)) = R$10,000.00<br />- Maturity Period (\(t\)) = 30 days = 1 month<br />- Discount Rate (\(d\)) = \(0.06\)<br /><br />\[ PV_1 = 10,000 \times (1 - 0.06 \times 1) = 10,000 \times 0.94 = 9,400 \]<br /><br />### **Duplicate 2:**<br />- Nominal Value (\(FV\)) = R$12,000.00<br />- Maturity Period (\(t\)) = 75 days = 2.5 months<br />- Discount Rate (\(d\)) = \(0.06\)<br /><br />\[ PV_2 = 12,000 \times (1 - 0.06 \times 2.5) = 12,000 \times 0.85 = 10,200 \]<br /><br />### **Duplicate 3:**<br />- Nominal Value (\(FV\)) = R$20,000.00<br />- Maturity Period (\(t\)) = 90 days = 3 months<br />- Discount Rate (\(d\)) = \(0.06\)<br /><br />\[ PV_3 = 20,000 \times (1 - 0.06 \times 3) = 20,000 \times 0.82 = 16,400 \]<br /><br />## Step 4: Calculate the Total Present Value Received<br />### Sum the present values of all duplicates to find the total amount received by the company.<br /><br />\[ \text{Total PV} = PV_1 + PV_2 + PV_3 = 9,400 + 10,200 + 16,400 = 36,000 \]
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