The 

SpenditSpendit 

Corporation borrowed 

$ 9 comma 900$9,900 

from Bank 

EaseEase. 

According to the terms of the​ loan, 

SpenditSpendit 

must pay the bank 

$ 381$381 

in interest every three months for the​ three-year life of the​ loan, with the principal to be repaid at the maturity of the loan. What effective annual rate 

​(EAR​) 

is 

SpenditSpendit 

​paying?

Question content area bottom

Part 1

The effective annual rate is 

enter your response here​%. 

** ​(Round to two decimal​ places.)

The **Effective Annual Rate (EAR)** represents the annual interest rate accounting for the effect of compounding. Given that SpenditSpendit is paying interest every three months, the compounding frequency is **quarterly**.

We can calculate the EAR using the following formula:

\[
EAR = \left(1 + \frac{i}{n}\right)^n - 1
\]

Where:
- $ i $ is the nominal annual interest rate
- $ n $ is the number of compounding periods per year

### Step 1: Calculate the nominal annual interest rate
- The loan amount is $ \$9,900 $.
- The interest payment per quarter is $ \$381 $.
- There are 4 quarters in a year.

The quarterly interest rate is:

\[
\text{Quarterly rate} = \frac{381}{9,900}
\]

We can multiply this by 4 to get the nominal annual interest rate $i$.

### Step 2: Calculate the EAR
Once we have $i$, we can substitute it into the EAR formula to compute the effective annual rate.

Let’s proceed with the calculations.The **Effective Annual Rate (EAR)** that SpenditSpendit is paying is **16.31%**.

Do you have any further questions or need more details on this calculation?

Here are 5 related questions to further your understanding:
1. How is the nominal annual interest rate different from the effective annual rate?
2. What is the impact of increasing the frequency of compounding on the EAR?
3. How would the EAR change if the loan had monthly payments instead of quarterly?
4. What formula would you use if the interest were compounded continuously?
5. How would the total interest paid over the life of the loan be calculated?

**Tip:** The EAR will always be higher than or equal to the nominal rate if compounding occurs more than once per year.

The Spendit Corporation borrowed $9,900 from Bank Ease. According to the terms of the loan, Spendit must pay the bank $381 in interest every three months for the three-year life of the loan, with the principal to be repaid at the maturity of the loan. What effective annual rate (EAR) is Spendit paying? (Round to two decimal places.)

Learn how to calculate the Effective Annual Rate (EAR) for a loan of $9,900 with quarterly interest payments of $381. Understand key financial concepts like compounding interest and the EAR formula. Suitable for college-level or advanced high school students.

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