I am about to start a new mortgage and wondered how to work out how much money I repay each month. I know the balance and I know the interst rate and I know that monthly payment so I suppose I need to calculate the interst and then subtract it from the monthly payment. How do I calculate the interest - I have the APR.
The APR is not good enough, you need to know the actual rate charged. The APR is usually equal to the annual equivalent of compounding the monthly rate, but it is then rounded to the nearest permille (tenth of a percent), which makes it impossible to recover the actual monthly rate from the APR with any great precision.
But if you're not too worried about precision, take the APR, add 1, then take the 12th root (i.e. raise to the power 1/12), and take away 1. So for an APR of 6.2%, raise 1.062 to the power 1/12 to get 1.005(ish), so the monthly rate is half a percent.
Usually it's easier. The lender will publish the nominal annual rate, e.g. 6%, and then the monthly rate is just a twelfth of that. That's assuming the lender applies payment to the loan account monthly. Some lenders actually apply yearly, so what they do is save up your 12 monthly payments in a secret account (non-interest-bearing of course) and then apply it.
Basically if you owe £100k and the interest rate is 6%pa or 0.5%pm, then the interest you pay in the 1st month will be £500. If your loan is over 300 months, your total monthly payment should be £100k x 0.005 / (1 - 1.005^-300) = £644.30, so you're paying off £144.30 in month 1. But don't worry, this amount will get bigger each month, slowly at first, because as the debt slowly shrinks, the interest each month will get less, leaving more of the fixed payment to pay off capital. In the 300th month, you'll pay only £3.20 interest and £641.10 capital.
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