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.
- 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
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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: \[ \text{New Principal} = 390,000 - 26,922 = 363,078 \]
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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: \[ \text{New Principal} = 363,078 - 29,076 = 334,002 \]
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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.
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