8. Erik needs to borrow $$ \$ 2000 $$. He has two loan options avallable to him. Loan $$ \mathrm{A}: ~ \$ 2000 $$ for three years at $$ 10 \% $$ per year, compounded semi-annually Loan Bc $$ \$ 2000 $$ for three years of $$ 9.2 \% $$ per year, compounded quarterly a) Make an educated GUESS which loan would cost Erik less interest. Explain your choice. Mar! are not given on the occuracy of your guess, but on how well you justify your choice. [2 marl

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**a) Educated Guess:**

**Loan B** would cost Erik less interest.

**Justification:**

- **Lower Nominal Interest Rate:** Loan B offers a **9.2%** annual interest rate compared to Loan A's **10%**. A lower interest rate generally means less interest accrued over time.
  
- **Compounding Frequency:** While Loan A compounds **semi-annually** (twice a year) and Loan B compounds **quarterly** (four times a year), which means Loan B compounds more frequently, the impact of the slightly higher compounding frequency is likely outweighed by the lower nominal rate.

- **Effective Interest Rate Consideration:** Even without exact calculations, the lower nominal rate of Loan B suggests that its overall effective interest rate would be less than Loan A's, resulting in less total interest paid over the three years.

Therefore, based on the lower interest rate and despite the higher compounding frequency, **Loan B** is expected to cost Erik less in interest.
**a) Educated Guess:** **Loan B** would cost Erik less interest because it has a lower annual interest rate of 9.2% compared to Loan A's 10%. Even though Loan B compounds more frequently (quarterly), the lower rate makes it the better choice. **Justification:** - **Lower Interest Rate:** Loan B's 9.2% is less than Loan A's 10%, meaning Erik would pay less interest overall. - **Compounding Frequency:** Although Loan B compounds more often (quarterly), the difference in interest rates makes Loan B more economical. Therefore, **Loan B** is expected to cost Erik less interest.

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