Question

Ann recently purchased a house for $220,000. she made a down payment of $20,000 and financed the balance over 15 years at 6%. if ann's first payment is due on october 1st of the current year, how much of her current year's payments will be applied to the outstanding principal on the loan?

Answer 1

To calculate the amount of Ann's current year's payments that will be applied to the outstanding principal on the loan, follow these steps: determine the loan amount after the down payment, use the formula for the monthly payment on a fixed-rate mortgage to find the monthly payment, and multiply the monthly payment by 12 to find the annual payment.

Step-by-step explanation:

To calculate how much of Ann's current year's payments will be applied to the outstanding principal on the loan, we first need to determine the amount of the loan after the down payment. Ann purchased the house for $220,000 and made a down payment of $20,000. Therefore, the loan amount is $220,000 - $20,000 = $200,000.

Next, we need to calculate the monthly payment. Since the loan is financed over 15 years (or 180 months) and the interest rate is 6% per year, we can use the formula for the monthly payment on a fixed-rate mortgage:

Monthly payment = Loan amount * (interest rate / 12) / (1 - (1 + interest rate / 12)^(-number of payments))

Plugging in the values, we get:

Monthly payment = $200,000 * (0.06 / 12) / (1 - (1 + 0.06 / 12)^(-180))

Using a calculator, this comes out to be approximately $1,557.16. Therefore, Ann's current year's payments will be $1,557.16 x 12 = $18,685.92.

Answer 2

To determine how much of Ann's current year's payments will be applied to the outstanding principal on the loan, we can use the loan amortization formula. The formula for calculating the monthly payment (PMT) on a fixed-rate mortgage is: PMT = P * (r(1+r)^n)/((1+r)^n - 1). After calculating this, you'll find the monthly payment amount. To determine how much of the first payment goes towards the principal, we can use the loan amortization schedule or formula. The formula for finding the principal portion of a loan payment is: Principal Payment = PMT - (Outstanding Loan Balance * Monthly Interest Rate).

To determine how much of Ann's current year's payments will be applied to the outstanding principal on the loan, we can use the loan amortization formula. The formula for calculating the monthly payment (PMT) on a fixed-rate mortgage is:

PMT = P * (r(1+r)^n)/((1+r)^n - 1)

Where:

• P is the loan amount (initial loan balance - down payment),
• r is the monthly interest rate (annual rate divided by 12 and expressed as a decimal),
• n is the total number of payments (loan term in years multiplied by 12).

In this case, Ann's loan amount (P) is the house price minus the down payment: P = $220,000 - $20,000 = $200,000.

The annual interest rate is 6%, so the monthly interest rate (r) is 0.06/12 = 0.005, and the loan term (n) is 15 years, which means n = 15 * 12 = 180 payments.

Now, plug these values into the formula to find the monthly payment: PMT = $200,000 * (0.005(1+0.005)^{180})/((1+0.005)^{180} - 1).

After calculating this, you'll find the monthly payment amount.

To determine how much of the first payment goes towards the principal, we can use the loan amortization schedule or formula. The formula for finding the principal portion of a loan payment is:

Principal Payment = PMT - (Outstanding Loan Balance * Monthly Interest Rate)

For the first payment, the outstanding loan balance is the original loan amount ($200,000), and the Monthly Interest Rate is $200,000 * 0.005. Plug these values into the formula to find the principal portion of the first payment.

Keep in mind that the interest for subsequent months will decrease as the outstanding balance decreases.