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What I don't get is not how interest is calculated but how the principal+interest is calculated per payment and why you payment always stays the same amount. For instance if I was loaned 12,000 interest free on a 1 year loan I would pay 1,000 a month for 12 months. 1,000 a month would go to the principal. So if I was given a loan for 12,000 at 10 % I'd assume it would be like this 12,000 x .10/12= $100 in interest Month 1: 1,000 principal + 100 interest for $1100 payment 11,000 x .10/12= 91.66 in interest Month 2: 1,000 principal + 91.66 in interest= 1091.66 payment. However if you actually took a loan like this here would be the real math Month 1: 954.99 and 100 interest Month 2: 962.95 and 92.04 Etc..... Why is it that your principal payment always changes. I don't quite get that aspect of a loan. Thanks
You're on the right track. You've noticed that if you pay 1/nth of the principal plus the periodic interest, your payment will go down each month. So - what if you made no payment? Well, your debt would grow at 0.10/12 per month. So somewhere Malakoff BETWEEN these payments ($0 and 1/nth + 0.10/12 * balance), there's a very delicate balancing point. Banks have special calculators and tables (called "amortization") that find this balancing point. At that point, the amount of principal you pay each period goes up a little bit as the interest goes down, keeping the payment constant. In fact, this function is built into Excel. It's called "PMT" and calculates a constant payment for a fixed interest rate and principal. You would NEVER be expected to do this by hand, though you could figure it out by successive estimation. In excel, the formula for the payment above is "=PMT(0.1/12,12,12000)", which gives $1054.99. So here's what your payments look like: Month 1: 12,000 * (1 + 0.10/12) = 12,100. Pay $1,054.99. New Balance 11,045.01 Month 2: 11,045.01 + 92.04 int = 11,137.05. Pay $1,054.99. New Balance 10,082.06 Month 3: 10,082.06 + 84.02 int = 10,166.08. Pay $1,054.99. New Balance 9,111.09 ... Month 12: 1,046.27 + 8.72 interest = 1,054,99. Make sense?