Question

On January​ 1, 2024, Southeastern Company purchased a building and signed a ten-year mortgage for $ 390000 at 8​%. The note will be paid in equal annual installments of $ 58122​, beginning January​ 1, 2025. Calculate the balance of Mortgages Payable after the payment of the third installment. ​ (Round any intermediate calculations and your final answer to the nearest​ dollar.)

Answer 1

To calculate the balance of Mortgages Payable after the payment of the third installment, we need to account for the interest and principal repayment with each installment.

1. **Understanding the Mortgage**:
- Principal amount: $390,000
- Annual interest rate: 8%
- Annual payment: $58,122
- Number of payments: 10

#### **Installment Payment Structure**
Each installment consists of a portion that goes toward paying off the interest and a portion that goes toward reducing the principal.

#### **Calculating the Interest and Principal for Each Installment**

1. **For the 1st Payment (at the end of Year 1)**
- Interest for Year 1:
\[
\text{Interest} = \text{Principal} \times \text{Interest Rate} = 390,000 \times 0.08 = 31,200
\]
- Principal repayment:
\[
\text{Principal} = \text{Annual Payment} - \text{Interest} = 58,122 - 31,200 = 26,922
\]
- New Principal after 1st Payment:
\[
\text{New Principal} = 390,000 - 26,922 = 363,078
\]

2. **For the 2nd Payment (at the end of Year 2)**
- Interest for Year 2:
\[
\text{Interest} = \text{New Principal} \times \text{Interest Rate} = 363,078 \times 0.08 = 29,046.24 \approx 29,046
\]
- Principal repayment:
\[
\text{Principal} = 58,122 - 29,046 = 29,076
\]
- New Principal after 2nd Payment:
\[
\text{New Principal} = 363,078 - 29,076 = 334,002
\]

3. **For the 3rd Payment (at the end of Year 3)**
- Interest for Year 3:
\[
\text{Interest} = \text{New Principal} \times \text{Interest Rate} = 334,002 \times 0.08 = 26,720.16 \approx 26,720
\]
- Principal repayment:
\[
\text{Principal} = 58,122 - 26,720 = 31,402
\]
- New Principal after 3rd Payment:
\[
\text{New Principal} = 334,002 - 31,402 = 302,600
\]

#### **Final Calculation**
Thus, the balance of Mortgages Payable after the payment of the third installment is
\[
\text{Mortgages Payable} = \text{New Principal} = 302,600
\]

### **Answer**
The balance of Mortgages Payable after the payment of the third installment is **$302,600**.