initial principal balance - 200,000
total interest paid - 279,017.80
years amortized - 30
payments/yr - 12
The formula for a standard mortgage is Payment * (1-vⁿ)/i = L
Where Payment is the monthly payment, v = 1/1+i, i is your effective interest rate, and L is the Loan Amount.
Total Interest paid is the Number of Payments you will make minus the loan amount. Let our Monthly Payment be P, so we have 360P - 200,000 = 279,017.8. Solving for P, we get 1330.61 for our monthly payment on the Loan.
Taking our original loan equation, we have
From here, you'd need logs/natural logs. Can you take it from here?
Also, to see more detail on a home loan payment proving 7% is your answer another way, use my mortgage calculator here: