**Consider two mortgage loans with the same principal and the same APR. Loan 1 is fixed for 30 years, and Loan 2 is fixed for 20 years. Which statement is true?**

Both loans will have the same monthly payments, but you’ ll pay less total interest with Loan 2.

Loan 1 will have lower monthly payments, but you’ll pay less total interest over the life of the loan.

Loan 2 will have higher monthly payments, but you’ll pay less total interest over the life of the loan.

**Answer:**

The only correct statement would be that Loan 2 will have higher monthly payments, but you’ll pay less total interest over the life of the loan.

We can see that the first statement is false by simplifying the question. Lets ignore APR and say I loaned you $100.and you had an option of paying back this loan in three equal payments of $33 (one payment every day for 3 days) or two equal payments of $50 (one payment every day for 2 days). Obviously you’ll need to pay back more per payment if you are taking out a loan (mortgage) for a shorter amount of time.

Now lets look at the second statement. with a mortgage you are constantly being charged interest on a principal (the mortgage). If you took out a shorter mortgage (one that lasted less years) you will be paying a higher amount each month, and consequently paying off more of your principal each month. Therefore every following month you will have less principal that will be accruing interest that you will therefore need to pay back. Another way to think about it is that at the end of 20 years, you could either have your mortgage paid off, or you could still owe about 1/3rd of your mortgage. Now, you are STILL borrowing money from the bank and they are still charging you interest on this money that you owe them.