To set up the amortization table, we can use the mortgage and interest formulas as follows:
Mortgage formula:
M = P [ i(1 + i)^n / (1 + i)^n - 1]
where M is the monthly payment, P is the principal (the amount borrowed), i is the monthly interest rate (APR divided by 12), and n is the total number of payments (20 years multiplied by 12 months per year).
Interest formula:
I = P * i
where I is the monthly interest payment, P is the remaining principal balance, and i is the monthly interest rate.
Using these formulas, we can set up the following amortization table for the first two months:
Month Payment Principal Interest Balance
1 $400,000
2
To fill in the table, we need to calculate the monthly payment (M) and the monthly interest payment (I) for the first month, and then use these values to calculate the principal payment for the first month. We can then subtract the principal payment from the initial balance to get the balance for the second month, and repeat the process to fill in the remaining columns.
To calculate the monthly payment (M), we can use the mortgage formula:
M = P [ i(1 + i)^n / (1 + i)^n - 1]
where P is the principal amount, i is the monthly interest rate, and n is the total number of payments.
Plugging in the given values, we get:
M = 400,000 [ 0.00279 (1 + 0.00279)^240 / (1 + 0.00279)^240 - 1]
M = $2,304.14
Therefore, the monthly payment is $2,304.14.
To calculate the interest payment for the first month, we can use the interest formula:
I = P * i
where P is the remaining principal balance and i is the monthly interest rate.
Plugging in the values for the first month, we get:
I = 400,000 * 0.00279
I = $1,116.00
Therefore, the interest payment for the first month is $1,116.00.
To calculate the principal payment for the first month, we can subtract the interest payment from the monthly payment:
Principal payment = Monthly payment - Interest payment
Principal payment = $2,304.14 - $1,116.00
Principal payment = $1,188.14
Therefore, the principal payment for the first month is $1,188.14.
To calculate the balance for the second month, we can subtract the principal payment from the initial balance:
Balance = Initial balance - Principal payment
Balance = $400,000 -$1,188.14
Balance = $398,811.86
Therefore, the balance for the second month is $398,811.86.
Using these values, we can complete the first two rows of the amortization table as follows:
Month Payment Principal Interest Balance
1 $2,304.14 $1,188.14 $1,116.00 $398,811.86
2
To fill in the remaining columns for the second month, we can repeat the process using the new balance of $398,811.86 as the principal amount for the second month. We can calculate the interest payment using the same method as before, and then subtract the interest payment from the monthly payment to get the principal payment. We can then subtract the principal payment from the balance to get the new balance for the third month, and repeat the process for the remaining months of the amortization period.