Question

4. When preparing for a business trip to China, Kaylee Putbrese determined she needed to bring $5.200.How much must she borrow for a simple discount note at 6% for 45 days?

Answer 1

Kaylee Putbrese must borrow approximately $5,160.92 for a simple discount note at a 6% interest rate for 45 days to have $5,200 at the end of the borrowing period.

Step-by-step explanation:

To determine how much Kaylee Putbrese must borrow for a simple discount note at 6% for 45 days to have $5,200 at the end of the period, we need to calculate the present value of the sum she needs. A simple discount note means that the interest is deducted from the principal when the loan is issued, and thus the borrower receives the present value.

To find this present value, we use the formula PV = FV / (1 + rt), where PV is the present value, FV is the future value (which is the amount needed at the end of the period), r is the interest rate, and t is the time period in years.

First, we convert the interest rate to a decimal by dividing it by 100:
6% / 100 = 0.06. Then we convert the time period from days to years by dividing by 365: 45/365 ≈ 0.1233 years.

Now we can calculate the present value:
PV = $5,200 / (1 + 0.06 * 0.1233) ≈ $5,200 / 1.007398 ≈ $5,160.92.

Therefore, Kaylee must borrow approximately $5,160.92 for a simple discount note at 6% for 45 days to end up with $5,200.

Answer 2

Case: Discount

Given:

Final value = $5200

discount rate= 6% for 45 days

Required: To find how much she must borrow to give $5200

Method:

Step 1: Let the amount to borrow be P

Step 2: If he borrows P and enjoys 6% discount, he will only be paying 94% of the value he borrow. This translates to:

`\begin{gathered} (94)/(100)* P=\text{ 5200} \\ P=\text{ 5200}*(100)/(94) \\ P=\text{ \$5531.91} \end{gathered}`

Final answer:

Kayle has to borrow $5531.91