Suppose you take out a home mortgage for $160000$ at a monthly interest rate of $0.5$%. If you make payments of $1200$ per month, after how many months will the loan balance be zero. Estimate the answer by graphing the sequence of loan balances and then obtain an exact answer.
I have thought to do the following:
As you have to pay $0.5$% for interest then in the first month you have to pay $0.5$% of $160000=800$ for interest and as you paid for $1200$, then for the house you gave $1200-800=400$, so $160000-400=159600$ was already owed and to know how much is left of the second month one does the same, takes out $0,5$% of $159600=798$ and thus paid interest $798$ and was due $159198$. This reasoning is fine? How can I generalize this and do what they ask of me in the problem? Thank you.