Bob bought a new log cabin for $70,000 at 8% interest for 30 years with no down payment. What is the balance of the loan after the 3 rd payment? You must prepare a 3 month amortization schedule.
To calculate the balance of the loan after the 3rd payment, we first need to calculate the monthly payment.
The formula to calculate the monthly payment for a loan is:
Monthly Payment = P * r * (1 + r)^n / ((1 + r)^n - 1),
where P is the principal (loan amount), r is the monthly interest rate, and n is the number of payments (in months).
Given:
Principal (P) = $70,000
Interest Rate (r) = 8% (converted to decimal by dividing by 100 and then by 12 for monthly)
Number of payments (n) = 30 years x 12 months/year = 360 months
r = 8% / 100 / 12 = 0.0067 (approx.)
Monthly Payment = $70,000 * 0.0067 * (1 + 0.0067)^360 / ((1 + 0.0067)^360 - 1)
≈ $515.20
Now, let's calculate the balance of the loan after the 3rd payment.
Month | Payment | Principal | Interest | Balance
--------------------------------------------------------
1 | $515.20 | $202.18 | $313.02 | $69,797.82
2 | $515.20 | $203.03 | $312.17 | $69,594.79
3 | $515.20 | $203.87 | $311.33 | $69,390.92
Therefore, the balance of the loan after the 3rd payment is $69,390.92.