Let's break down the problem step by step: ### **Step 1: Understand the terms** - **Loan interest rate = LIBOR + 26 basis points** - 1 basis point = 0.01%, so 26 bps = 0.26% - **The rate for each week is based on LIBOR from the *previous* week** - **Maximum rate: 2.17%** - **Minimum rate: 1.77%** ### **Step 2: Find LIBOR for the week prior to week 2** - **Week 2's interest rate uses LIBOR from Week 1** - Week 1 LIBOR = **1.97%** ### **Step 3: Calculate the raw rate before caps/floors** \[ \text{Raw rate} = \text{LIBOR (previous week)} + 0.26\% \] \[ = 1.97\% + 0.26\% = 2.23\% \] ### **Step 4: Apply the maximum/minimum cap** - The maximum allowed rate is **2.17%** - The minimum allowed rate is **1.77%** - Our raw rate (2.23%) is above the maximum, so the **actual rate for week 2 is capped at 2.17%** ### **Step 5: Final Answer** \[ \boxed{2.17\%} \] --- **The rate of interest for week 2 is:** \[ \boxed{2.17\%} \]

Let's carefully work through the problem step-by-step, ensuring clarity at each stage. --- ### **Given Data:** - The loan's interest rate = LIBOR + 0.26% (or 26 basis points) - Weekly adjustment based on previous week's LIBOR - Maximum annual rate = 2.17% - Minimum annual rate = 1.77% - Week 2 LIBOR = 1.69% - Week 1 LIBOR = 1.97% - Week 3 LIBOR = 1.45% - Week 4 LIBOR = 1.34% - Week 5 LIBOR = 1.63% - Week 6 LIBOR = 1.63% - Week 7 LIBOR = 1.72% - Week 8 LIBOR = 1.89% - Week 9 LIBOR = 1.92% --- ### **Step 1: Determine the rate for Week 2** **Note:** The rate for each week is based on the previous week's LIBOR. - For **Week 2**, the LIBOR used is **Week 1's LIBOR = 1.97%** ### **Step 2: Calculate the raw interest rate** \[ \text{Raw rate} = \text{Week 1 LIBOR} + 0.26\% \] \[ = 1.97\% + 0.26\% = 2.23\% \] ### **Step 3: Apply caps and floors** - The **maximum allowed rate** is **2.17%** - The **minimum allowed rate** is **1.77%** Since the raw rate **(2.23%)** exceeds the maximum cap **(2.17%)**, the **interest rate for Week 2** is **capped at 2.17%**. --- ### **Final answer:** **The interest rate for Week 2 is:** \[ \boxed{2.17\%} \] --- ### **Summary:** - **Week 2 LIBOR:** 1.97% - **Raw rate (LIBOR + 0.26%):** 2.23% - **Capped rate (max 2.17%):** **2.17%** Feel free to ask for calculations for other weeks!

Let's carefully determine the interest rate for week 2, following all steps with clear explanations. --- ### **Step 1: Understand the problem** - The loan interest rate each week = **LIBOR (from the previous week) + 0.26% (26 basis points)** - The rate **cannot** go below **1.77%** or above **2.17%** - For **Week 2**, the **LIBOR used** is the **Week 1 LIBOR**. --- ### **Step 2: Find the relevant LIBOR** - **Week 1 LIBOR** = **1.97%** --- ### **Step 3: Calculate the raw interest rate before caps** \[ \text{Raw rate} = \text{LIBOR (Week 1)} + 0.26\% \] \[ = 1.97\% + 0.26\% = 2.23\% \] --- ### **Step 4: Apply the maximum and minimum caps** - **Maximum rate** = 2.17% - **Minimum rate** = 1.77% Since **2.23%** exceeds the maximum cap **(2.17%)**, the **interest rate for Week 2 is capped at 2.17%**. --- ### **### Final Answer:** **The interest rate for Week 2 is:** \[ \boxed{2.17\%} \] --- ### **Summary:** | Detail | Value | |---------|---------| | LIBOR (Week 1) | 1.97% | | Raw Rate (Week 2) | 2.23% | | **Capped Rate** | **2.17%** | This approach ensures the interest rate respects the contractual maximum.

Let's work through the problem step-by-step with detailed calculations, formulas, and explanations. --- ### **Given Data:** | Week | LIBOR (%) | |---------|---------| | 1 | 1.97 | | 2 | 1.69 | | 3 | 1.45 | | 4 | 1.34 | | 5 | 1.63 | | 6 | 1.63 | | 7 | 1.72 | | 8 | 1.89 | | 9 | 1.92 | **Additional information:** - The **interest rate** for each week = **LIBOR of the previous week + 0.26% (26 basis points)** - **Cap on interest rate (annualized):** 2.17% - **Floor on interest rate (annualized):** 1.77% --- ### **Step 1: Determine the LIBOR for the previous week for Week 2** - Since the rate for Week 2 depends on Week 1 LIBOR: \[ \text{LIBOR}_{\text{Week 1}} = 1.97\% \] --- ### **Step 2: Calculate raw weekly interest rate for Week 2** \[ \text{Raw rate} = \text{LIBOR}_{\text{Week 1}} + 0.26\% \] \[ = 1.97\% + 0.26\% = 2.23\% \] --- ### **Step 3: Apply caps and floors** - The **interest rate** is **annualized**, but the cap and floor are given directly as percentages (assuming they are annual rates). For weekly rates, the same caps apply directly because the problem states the maximum and minimum **annual** rates, and the weekly rate is adjusted accordingly. - Since **2.23%** exceeds the **maximum** of **2.17%**, **we cap** the interest rate at **2.17%**. \[ \boxed{\text{Interest rate for Week 2} = \min(\max(\text{raw rate}, \text{floor}), \text{cap})} \] Applying the formula: \[ \boxed{ \text{Interest rate for Week 2} = \min(\max(2.23\%, 1.77\%), 2.17\%) = 2.17\% } \] --- ### **Final Answer:** \[ \boxed{ \text{Interest rate for Week 2} = \mathbf{2.17\%} } \] --- ### **Summary of calculations:** - **LIBOR (Week 1):** 1.97% - **Raw rate (Week 2):** 1.97% + 0.26% = 2.23% - **Capped rate (max 2.17%):** 2.17% - **Interest rate Week 2:** **2.17%** --- If you'd like, I can perform similar calculations for other weeks or clarify any parts further!

Certainly! Let's perform a detailed, step-by-step calculation of the interest rate for each week, based on the provided LIBOR rates and the loan terms. --- ## Given Data Summary | Week | LIBOR (%) | Notes | |--------|-----------|-----------------------------------------| | 1 | 1.97 | Starting point | | 2 | 1.69 | To be calculated based on Week 1 LIBOR | | 3 | 1.45 | Based on Week 2 LIBOR | | 4 | 1.34 | Based on Week 3 LIBOR | | 5 | 1.63 | Based on Week 4 LIBOR | | 6 | 1.63 | Based on Week 5 LIBOR | | 7 | 1.72 | Based on Week 6 LIBOR | | 8 | 1.89 | Based on Week 7 LIBOR | | 9 | 1.92 | Based on Week 8 LIBOR | - **Interest rate formula per week:** \[ \text{Interest Rate}_\text{week} = \text{LIBOR}_\text{previous week} + 0.26\% \] - **Caps and floors:** \[ \text{Max annual rate} = 2.17\% \] \[ \text{Min annual rate} = 1.77\% \] --- ## Step-by-Step Calculations ### **Week 2** - **LIBOR used:** Week 1 LIBOR = 1.97% \[ \text{Raw rate} = 1.97\% + 0.26\% = 2.23\% \] - **Apply caps/floors:** \[ \text{Capped rate} = \min(\max(2.23\%, 1.77\%), 2.17\%) = 2.17\% \] **Result for Week 2:** **2.17%** --- ### **Week 3** - **LIBOR used:** Week 2 LIBOR = 1.69% \[ \text{Raw rate} = 1.69\% + 0.26\% = 1.95\% \] - **Apply caps/floors:** \[ \text{Capped rate} = \min(\max(1.95\%, 1.77\%), 2.17\%) = 1.95\% \] **Result for Week 3:** **1.95%** --- ### **Week 4** - **LIBOR used:** Week 3 LIBOR = 1.45% \[ \text{Raw rate} = 1.45\% + 0.26\% = 1.71\% \] - **Apply caps/floors:** \[ \text{Capped rate} = \min(\max(1.71\%, 1.77\%), 2.17\%) = 1.77\% \] (Here, since 1.71% < 1.77%, we use the floor) **Result for Week 4:** **1.77%** --- ### **Week 5** - **LIBOR used:** Week 4 LIBOR = 1.34% \[ \text{Raw rate} = 1.34\% + 0.26\% = 1.60\% \] - **Apply caps/floors:** \[ \text{Capped rate} = \min(\max(1.60\%, 1.77\%), 2.17\%) = 1.77\% \] (1.60% < 1.77%) **Result for Week 5:** **1.77%** --- ### **Week 6** - **LIBOR used:** Week 5 LIBOR = 1.63% \[ \text{Raw rate} = 1.63\% + 0.26\% = 1.89\% \] - **Apply caps/floors:** \[ \text{Capped rate} = \min(\max(1.89\%, 1.77\%), 2.17\%) = 1.89\% \] **Result for Week 6:** **1.89%** --- ### **Week 7** - **LIBOR used:** Week 6 LIBOR = 1.63% \[ \text{Raw rate} = 1.63\% + 0.26\% = 1.89\% \] - Same as Week 6: \[ \boxed{1.89\%} \] **Result for Week 7:** **1.89%** --- ### **Week 8** - **LIBOR used:** Week 7 LIBOR = 1.72% \[ \text{Raw rate} = 1.72\% + 0.26\% = 1.98\% \] - **Apply caps/floors:** \[ \min(\max(1.98\%, 1.77\%), 2.17\%) = 1.98\% \] **Result for Week 8:** **1.98%** --- ### **Week 9** - **LIBOR used:** Week 8 LIBOR = 1.89% \[ \text{Raw rate} = 1.89\% + 0.26\% = 2.15\% \] - **Apply caps/floors:** \[ \min(\max(2.15\%, 1.77\%), 2.17\%) = 2.15\% \] **Result for Week 9:** **2.15%** --- ## **Summary of Weekly Interest Rates** | Week | LIBOR used (from previous week) | Raw rate (LIBOR + 0.26%) | Capped/Adjusted Rate | |---------|------------------------------|-------------------------|----------------------| | 2 | 1.97% | 2.23% | **2.17%** (max cap) | | 3 | 1.69% | 1.95% | 1.95% | | 4 | 1.45% | 1.71% | **1.77%** (floor) | | 5 | 1.34% | 1.60% | **1.77%** (floor) | | 6 | 1.63% | 1.89% | 1.89% | | 7 | 1.63% | 1.89% | 1.89% | | 8 | 1.72% | 1.98% | 1.98% | | 9 | 1.89% | 2.15% | 2.15% | --- ## **Conclusion** - Each week’s interest rate is calculated based on the previous week's LIBOR plus 0.26%, then capped or floored to stay within the 1.77%–2.17% range. - Week 2's rate, for example, is **2.17%** due to the cap. Let me know if you'd like me to clarify any step further!