<prompt> Human: Jay Z and Beyonce took out a 52.8 M mortgage on their new 88 M home Their net worth is a combined 1.16 B. Why did they take out a mortgage when they could seemingly readily pay for the house up front?At first I was thinking with a low enough interest rate they could invest the money and, with high enough returns, simply generate a profit off the mortgage. But after running the numbers, even at 1 annual interest, they would have to generate at least an average of 13.6 return on investment for that strategy to be profitable. 1-principaltotal mortgage paymentsEdit: Does someone want to help me figure out what I was calculating? I figured the monthly payment, PMT, at 1 annual I got 169,826 multiplied by 360 months, N, minus the original principal, P, is the total amount in excess of principal that theyd have to pay due to interest. Divide that by how much they did pay to get the percentage of what they paid that went to interest payments. PMT N - PPMT NAssistant: But after running the numbers, even at 1 annual interest, they would have to generate at least an average of 13.6 return on investment for that strategy to be profitable. 1-principaltotal mortgage paymentsYour formula is wrong. They only need to beat 1 annual returns to outrun a 1 mortgage rate ignoring taxes.Human: Im not sure what I was calculating, but what would be PMT N - P PMT N? As in, the total amount they would pay in the end paying monthly payments, subtracted from the principal loan, as a fraction of the total amount they had to pay.Assistant: Are you trying to account for monthly compounding? Your rate is assuming a 1 monthly interest, not a 1 yearly.Even when using monthly compounding, your total expense on 1,000 with a 1 YTD interest will be 10.46 thus the compounding makes the rate actually 1.46Human: I used, 112 in my PMT formula, giving a monthly payment of 169,826 on the 52.8M principal. Did I mix up the rates elsewhere?  <response>: I suspect youre mixing up interest and principal in terms of what you need to beat. You only need to beat the interest portion of the payment in terms of other assets to make the mortgage worth it - assuming that the property holds value or increases.For example, my mortgage is at 3.625 which basically means payments on principal give me a guaranteed rate of return of 3.625, but if I have that money in investments performing at 4 Im better off. 