Ina is negotiating a mortgage of $145 000 for her new house. Determine Ina's monthly payments for a mortgage at 5% annum, compounded semi-annually, amortized over 25 years. How much will Ina pay over the 25 years to pay off this mortgage?

To use the formula for a series of payments, such as carpayments, and mortgages, the period of compounding and the period of payments must be the same.

Yours has the interest compounded semi-annually, and the payments are monthly, which does not match up
So we have to find the monthly rate equalent to a rate of 5% per annum compounded semi-annually

let the monthly rate be i , then
(1+i)^6 = 1.025
1+i = 1.025^(1/6) = 1.004123915
i = .0041239... ----- I stored that in my calculator

let the payment be P

P(1 - 1.0041239..^-300)/.0041239... = 145000
...
P = $843.33

To determine Ina's monthly payments for the mortgage, we can use the formula for the monthly payment on a mortgage:

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

Where:
P = monthly payment
r = monthly interest rate
A = loan amount
n = total number of payments

First, let's calculate the monthly interest rate:
The annual interest rate is 5%, compounded semi-annually. To convert it to a monthly rate, we divide it by 12 (the number of months in a year). Since the interest is compounded semi-annually, we need to divide the annual interest rate by 2.

r = (5% / 12) / 100
r = 0.00416667

Next, let's calculate the total number of payments:
The mortgage is amortized over 25 years, which means there will be 25 * 12 = 300 monthly payments.

n = 300

Now, let's substitute the values into the formula to find Ina's monthly payments:

P = (0.00416667 * 145000) / (1 - (1 + 0.00416667)^(-300))
P ≈ $866.53

Therefore, Ina's monthly mortgage payment will be approximately $866.53.

To calculate how much she will pay over the 25 years to pay off the mortgage, we can multiply the monthly payment (P) by the total number of payments (n):

Total payment = P * n
Total payment = $866.53 * 300
Total payment ≈ $259,959

Therefore, Ina will pay approximately $259,959 over the 25 years to pay off this mortgage.