The compound interest a teacher would have to pay the bank if she borrows

150 000 for 10 years at 12.5% per annum

To calculate the compound interest, we can use the following formula:

A = P(1 + r/n)^(nt)

Where:
A = Total amount including interest
P = Principal amount (initial loan amount)
r = Annual interest rate (as a decimal)
n = Number of times that interest is compounded per year
t = Number of years

In this case,
P = $150,000
r = 12.5% = 0.125 (convert percentage to decimal)
n = 1 (interest is compounded annually)
t = 10 years

Substituting the values into the formula:

A = 150,000(1 + 0.125/1)^(1*10)
A = 150,000(1.125)^10

Now, we can calculate A:

A = 150,000(1.125)^10
A ≈ 150,000(3.172)

Therefore, the total amount the teacher would have to pay back including compound interest would be approximately $475,800.

To calculate the compound interest, we can subtract the principal amount from the total amount:

Compound Interest = Total Amount - Principal Amount
Compound Interest = $475,800 - $150,000
Compound Interest = $325,800

So, the teacher would have to pay approximately $325,800 as compound interest over the 10-year period.