The problem describes a debt to be amortized.

A man buys a house for $350,000. He makes a $150,000 down payment and amortizes the rest of the debt with semiannual payments over the next 12 years. The interest rate on the debt is 11%, compounded semiannually. (Round your answers to the nearest cent.)
(a) Find the size of each payment.
$ 1

(b) Find the total amount paid over the life of the loan (including the down payment).
$ 2

(c) Find the total interest paid over the life of the loan.
$ 3

To solve this problem, we need to use the formula for calculating the payment amount on an amortizing loan. The formula is:

Payment Amount = Principal x (r(1+r)^n) / ((1+r)^n - 1)

where:
- Principal is the remaining debt after the down payment
- r is the semiannual interest rate
- n is the total number of payments

(a) Find the size of each payment:

First, we need to calculate the remaining debt after the down payment:
Remaining Debt = Total Price - Down Payment
Remaining Debt = $350,000 - $150,000
Remaining Debt = $200,000

Next, let's calculate the r value by dividing the annual interest rate by 2 (since it is compounded semiannually):
r = Annual Interest Rate / 2
r = 11% / 2
r = 0.11 / 2
r = 0.055

Now, let's calculate the total number of payments. Since the payments are made semiannually for 12 years, there will be 2 payments per year for a total of 24 payments:
n = 2 payments/year x 12 years
n = 24

Using the formula, we can calculate the payment amount:
Payment Amount = $200,000 x (0.055(1+0.055)^24) / ((1+0.055)^24 - 1)

Now, let's do the calculations:

Payment Amount = $200,000 x (0.055(1+0.055)^24) / ((1+0.055)^24 - 1)
Payment Amount = $200,000 x (0.055(1.055)^24) / ((1.055)^24 - 1)
Payment Amount = $200,000 x (0.055(1.8812)) / (1.8812 - 1)
Payment Amount = $200,000 x 0.10347 / 0.8812
Payment Amount = $200,000 x 0.11730
Payment Amount = $23,460

Therefore, the size of each payment is $23,460.

(b) Find the total amount paid over the life of the loan (including the down payment):

Total Amount Paid = Down Payment + (Payment Amount x Total Number of Payments)
Total Amount Paid = $150,000 + ($23,460 x 24)

Now, let's do the calculations:

Total Amount Paid = $150,000 + ($23,460 x 24)
Total Amount Paid = $150,000 + $563,040
Total Amount Paid = $713,040

Therefore, the total amount paid over the life of the loan, including the down payment, is $713,040.

(c) Find the total interest paid over the life of the loan:

Total Interest Paid = Total Amount Paid - Remaining Debt
Total Interest Paid = $713,040 - $200,000

Now, let's do the calculations:

Total Interest Paid = $713,040 - $200,000
Total Interest Paid = $513,040

Therefore, the total interest paid over the life of the loan is $513,040.