Final answer:
Sam's monthly mortgage payment can be calculated using the annuity formula. A smaller portion of the first payment will go towards the principal, which is a common practice in amortized loans to compensate lenders for risk upfront. Fairness is subjective but it follows industry standards.
Step-by-step explanation:
To calculate the monthly mortgage payment for Sam's fully amortized loan of 10 million over 20 years at a 5% fixed mortgage rate, we use the formula for an annuity. The formula is P = (r*PV)/(1-(1+r)^-n), where P is the monthly payment, r is the monthly interest rate, PV is the present value of the loan (10 million), and n is the total number of payments. In this case, r is 0.05/12 (monthly interest rate) and n is 20*12 (total number of monthly payments over 20 years).
The percentage of the first payment that goes towards the principal is found by subtracting the interest portion of the first payment from the total monthly payment and then dividing by the total monthly payment. This is typically a smaller portion as earlier payments on fully amortized loans are more interest-heavy. As for whether it is fair to Sam, this is subjective.