\n
Final Note: Some High School Math
\nYou probably don't know how to calculate compound interest payments. Just figuring out how to use Excel's formulae is pretty nasty. The underlying math is very simple.\n\nLet's suppose you're depositing $1 per month into an account that accrues monthly compounding interest of I%. The amount of money you accrue is a geometric series, i.e. after N months:\n\n$1 (today's deposit) + $1 * (1 + I) ^ 1 + $1 * (1 + I) ^ 2 + ... $1 + (1 + I) ^ (N - 1)\n\nOR\n\n1 + 1 * R + 1 * R^2 + ... + 1 * R^(N-1) (where R = 1 + I)\n\nThere's a neat formula for calculating this (which I learned in High School; your mileage may vary):\n\nS = ( 1 - R ^ N ) / ( 1 - R )\n\nYou may have seen this with an \"A\" out the front, but I've simplified this by assuming the initial term is 1.\n\nNow this tells us how much we'll have \"paid back\" at an interest rate of I with payments of $1 over N months.\n\nWe can work out how much we owe as: T = P * (1 + I) ^ N. (This is the principle -- i.e. loan amount -- compounded at the same rate for N months.)\n\nSo, to find out the monthly payment, divide this result by the earlier sum:\n\nPayment = T / S.\n\nYou can quickly verify this formula on your mortgage with one more piece of information: in the US lenders are legally allowed to misrepresent interest rates. In many other countries, lenders must either give you an APR (\"Annual Percentage Rate\" which is to say \"Interest Rate when I don't flat out lie\"), but in the US they're allowed to say 12%, when in fact they mean 1% compounded monthly, which is significantly more (12.7%).\n\nThat's it.","$updatedAt":"2024-06-05T09:49:11.148+00:00",path:"mortgage-brokers",_created:"2024-07-09T20:33:38.977Z",id:"123",_modified:"2024-07-09T20:33:38.977Z","$id":"123",_path:"post/path=mortgage-brokers"}}