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(Related to Checkpoint 9.1)

Floating Rate Loans

The Bensington Glass Company entered into a loan agreement with the firm's bank to finance the firm's working capital. The loan called for a floating rate that was 27 basis points (0.27 percent) over an index based on LIBOR. In addition, the loan adjusted weekly based on the closing value of the index for the previous week and had a maximum annual rate of 2.21 percent and a minimum of 1.72 percent.

Calculate the rate of interest for weeks 2 through 10.

\begin{tabular}{|cc|}
\hline
Date & LIBOR \\
\hline
Week 1 & [tex]$1.96\%$[/tex] \\
Week 2 & [tex]$1.08\%$[/tex] \\
Week 3 & [tex]$1.53\%$[/tex] \\
Week 4 & [tex]$1.31\%$[/tex] \\
Week 5 & [tex]$1.50\%$[/tex] \\
Week 6 & [tex]$1.63\%$[/tex] \\
Week 7 & [tex]$1.74\%$[/tex] \\
Week 8 & [tex]$1.94\%$[/tex] \\
\hline
\end{tabular}

The rate of interest for week 2 is [tex]$\square$[/tex] 9. (Round to two decimal places)



Answer :

GinnyAnswer
Let's break down the calculation of the rate of interest for weeks 2 through 10 step-by-step.

The fundamental points to consider are:
1. The interest rate for the loan is the LIBOR rate plus 0.27% (27 basis points).
2. There is a maximum interest rate of 2.21% and a minimum interest rate of 1.72%.

We'll calculate the interest rates for weeks 2 through 10 using the given LIBOR rates for each week.

### Detailed Calculations:

Interest Rate Calculation Formula:
[tex]\[ \text{Interest Rate} = \min(\max(\text{LIBOR Rate} + 0.27\%, 1.72\%), 2.21\%) \][/tex]

Step-by-Step Calculations:

1. Week 2:
- LIBOR: 1.08%
- Floating Rate: 1.08% + 0.27% = 1.35%
- Apply minimum and maximum constraints: 1.72% (as 1.72% < 1.35% < 2.21%)
- Result: 1.72%

2. Week 3:
- LIBOR: 1.53%
- Floating Rate: 1.53% + 0.27% = 1.80%
- Apply minimum and maximum constraints: 1.80% (as 1.72% < 1.80% < 2.21%)
- Result: 1.80%

3. Week 4:
- LIBOR: 1.31%
- Floating Rate: 1.31% + 0.27% = 1.58%
- Apply minimum and maximum constraints: 1.72% (as 1.72% < 1.58% < 2.21%)
- Result: 1.72%

4. Week 5:
- LIBOR: 1.50%
- Floating Rate: 1.50% + 0.27% = 1.77%
- Apply minimum and maximum constraints: 1.77% (as 1.72% < 1.77% < 2.21%)
- Result: 1.77%

5. Week 6:
- LIBOR: 1.63%
- Floating Rate: 1.63% + 0.27% = 1.90%
- Apply minimum and maximum constraints: 1.90% (as 1.72% < 1.90% < 2.21%)
- Result: 1.90%

6. Week 7:
- LIBOR: 1.74%
- Floating Rate: 1.74% + 0.27% = 2.01%
- Apply minimum and maximum constraints: 2.01% (as 1.72% < 2.01% < 2.21%)
- Result: 2.01%

7. Week 8:
- LIBOR: 1.94%
- Floating Rate: 1.94% + 0.27% = 2.21%
- Apply minimum and maximum constraints: 2.21% (as 2.21% is the maximum constraint)
- Result: 2.21%

To summarize, the interest rates for weeks 2 to 10 (taking the available LIBOR rates into account for subsequent weeks) are:
- Week 2: 1.72%
- Week 3: 1.80%
- Week 4: 1.72%
- Week 5: 1.77%
- Week 6: 1.90%
- Week 7: 2.01%
- Week 8: 2.21%

Thus, the rate of interest for weeks 2 to 10 are, rounded to two decimal places:
[tex]\[ [1.72\%, 1.80\%, 1.72\%, 1.77\%, 1.90\%, 2.01\%, 2.21\%] \][/tex]

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