First, we need to calculate the monthly mortgage payment. The formula for the monthly payment on a loan is:

P = [r*PV] / [1 - (1 + r)^-n]

Where:
P = monthly payment
r = monthly interest rate
PV = loan amount (present value)
n = total number of payments

Given:
PV = $300,000
r = 6% p.a. compounded monthly = 6%/12 = 0.5% per month = 0.005 (in decimal form)
n = 30 years * 12 months/year = 360 months

Substituting the given values into the formula:

P = [0.005 * $300,000] / [1 - (1 + 0.005)^-360]
P = $1,500 / [1 - 0.233849]
P = $1,500 / 0.766151
P ≈ $1,955.14

This is the monthly mortgage payment.

Next, we need to calculate the total amount of interest paid in the first year. The interest portion of each monthly payment is the remaining balance of the loan times the monthly interest rate. At the beginning, the remaining balance of the loan is the full loan amount.

So, the interest paid in the first month is:

Interest_1 = $300,000 * 0.005 = $1,500

After the first payment, the remaining balance of the loan is reduced by the principal portion of the payment, which is the total payment minus the interest:

Principal_1 = P - Interest_1 = $1,955.14 - $1,500 = $455.14

So, the remaining balance after the first payment is:

Balance_1 = $300,000 - Principal_1 = $300,000 - $455.14 = $299,544.86

Then, the interest paid in the second month is:

Interest_2 = Balance_1 * 0.005 = $299,544.86 * 0.005 = $1,497.72

We can continue this process for each of the 12 months of the first year. However, to simplify, we can approximate the interest paid in the first year as the interest paid in the first month times 12:

Interest_first_year ≈ Interest_1 * 12 = $1,500 * 12 = $18,000

Therefore, the amount of interest you will pay during the first year is closest to $18,000.

Question

First, we need to calculate the monthly mortgage payment. The formula for the monthly payment on a loan is:

P = [r*PV] / [1 - (1 + r)^-n]

Where:
P = monthly payment
r = monthly interest rate
PV = loan amount (present value)
n = total number of payments

Given:
PV = $300,000
r = 6% p.a. compounded monthly = 6%/12 = 0.5% per month = 0.005 (in decimal form)
n = 30 years * 12 months/year = 360 months

Substituting the given values into the formula:

P = [0.005 * $300,000] / [1 - (1 + 0.005)^-360]
P = $1,500 / [1 - 0.233849]
P = $1,500 / 0.766151
P ≈ $1,955.14

This is the monthly mortgage payment.

Next, we need to calculate the total amount of interest paid in the first year. The interest portion of each monthly payment is the remaining balance of the loan times the monthly interest rate. At the beginning, the remaining balance of the loan is the full loan amount.

So, the interest paid in the first month is:

Interest_1 = $300,000 * 0.005 = $1,500

After the first payment, the remaining balance of the loan is reduced by the principal portion of the payment, which is the total payment minus the interest:

Principal_1 = P - Interest_1 = $1,955.14 - $1,500 = $455.14

So, the remaining balance after the first payment is:

Balance_1 = $300,000 - Principal_1 = $300,000 - $455.14 = $299,544.86

Then, the interest paid in the second month is:

Interest_2 = Balance_1 * 0.005 = $299,544.86 * 0.005 = $1,497.72

We can continue this process for each of the 12 months of the first year. However, to simplify, we can approximate the interest paid in the first year as the interest paid in the first month times 12:

Interest_first_year ≈ Interest_1 * 12 = $1,500 * 12 = $18,000

Therefore, the amount of interest you will pay during the first year is closest to $18,000.

Knowee AI · Accepted Answer