Question
Multiple Choice Question On January 1,2018 , Burrows, Inc. received \( \$ 8,900 \) and agreed to pay \( \$ 10,000 \) on January 1,2020 . The market rate of interest is \( 6 \% \) compounded annually. For the 2nd year of this note (f.e., ended December 31,2019 ), Interest Expense on this note payable equals._ (Round to the nearest \( \$ 1 \).) (i) \( \$ 600 \) O \( \$ 0 \) ( \( \$ 566 \) 0
Ask by Hall Higgins. in the United States
Feb 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The interest expense for the second year is \( \$566 \).
Solution
To calculate the Interest Expense for the second year of the note payable, we need to follow these steps:
1. **Identify the principal amount and interest rate**:
- The principal amount (the present value) is \( P = 8,900 \).
- The future value (the amount to be paid) is \( F = 10,000 \).
- The interest rate is \( r = 6\% \) or \( 0.06 \).
2. **Calculate the interest expense for the first year (2018)**:
The interest expense for the first year can be calculated using the formula:
\[
\text{Interest Expense} = P \times r
\]
where \( P \) is the principal amount at the beginning of the year.
3. **Calculate the principal amount at the beginning of the second year (2019)**:
After the first year, the principal amount will be increased by the interest expense calculated for the first year.
4. **Calculate the interest expense for the second year (2019)**:
The interest expense for the second year will be calculated using the new principal amount at the beginning of the second year.
Let's perform these calculations step by step.
### Step 1: Calculate Interest Expense for the First Year (2018)
\[
\text{Interest Expense}_{2018} = 8,900 \times 0.06
\]
### Step 2: Calculate the Principal Amount at the Beginning of 2019
\[
\text{Principal}_{2019} = 8,900 + \text{Interest Expense}_{2018}
\]
### Step 3: Calculate Interest Expense for the Second Year (2019)
\[
\text{Interest Expense}_{2019} = \text{Principal}_{2019} \times 0.06
\]
Now, let's calculate these values.
1. Calculate the interest expense for the first year:
\[
\text{Interest Expense}_{2018} = 8,900 \times 0.06 = 534
\]
2. Calculate the principal amount at the beginning of 2019:
\[
\text{Principal}_{2019} = 8,900 + 534 = 9,434
\]
3. Calculate the interest expense for the second year:
\[
\text{Interest Expense}_{2019} = 9,434 \times 0.06
\]
Now, let's calculate the final interest expense for the second year.
\[
\text{Interest Expense}_{2019} = 9,434 \times 0.06 = 566.04
\]
Rounding to the nearest dollar, the interest expense for the second year (2019) is approximately \( \$ 566 \).
Thus, the answer is:
**\( \$ 566 \)**.
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Simplify this solution Mind Expander
To calculate the Interest Expense for the second year of the note, we first need to determine the effective interest for the initial amount received and what it will grow into at the end of the second year. After one year, the amount owed at a 6% interest rate on the initial \( \$ 8,900 \) would be: \[ \text{Amount after Year 1} = 8,900 \times (1 + 0.06) = 8,900 \times 1.06 = 9,434 \] Now, for the second year, we calculate the interest on this new amount: \[ \text{Interest Expense for Year 2} = 9,434 \times 0.06 = 566.04 \] Rounding this to the nearest dollar gives us \( \$ 566 \) as the Interest Expense for the second year. Thus, the answer is \( 566 \).
