# Interest Calculation - help?

I require a bit of bit in calculating interest given an interest rate.
Hopefully it will help me understand how loans work.
I have a loan which has a monthly rate of 0.49% per month.
If for arguments sake, the loan is for 5000 paid back monthly over 36
months and to pay it off early a few months in, I have to pay 1 months
interest as a penalty. How do I work out how much that penalty is? Is
it 0.49% of the amount borrowed, 0.49% of the total amount borrowed
including the interest (eg. final amount payable) ... ?
NB. I am thinking of extending my mortgage to pay off the loan as I
will benefit from a better rate. Before I do that I need to know if I
will pay less interest that way since a) the mortgage term is over a
much monger period, b) i need to calculate the amount of interest
currently payable on my loan first and compare that to the additional
interest on the mortgage if i decide to extend it.
Speak into a paper bag first, then carefully sort out the words before committing them into type. Then readers won't have to guess what you mean by the likes of "a bit of bit".
It will tell you in the loan agreement. Depending on circumstances, it may be 0.49% of the original amount borrowed, or only of the sum repaid early.
The former (proportion of amount originally borrowed) tends to be the case where special discount deals are involved. For example, I have a flexible mortgage loan which involves a stepped 3-year discount where I get a discount of 1% off SVR in the first year, 0.75% in the 2nd, and 0.5% in the 3rd. Being flexible, I can over pay as much as I like without penalty, so long as a minimum of (I think) £100 remains outstanding, but if I redeem completely, I must pay a penalty of 3% of the original amount borrowed if I redeem in year 1, or 2%/1% if in year 2/3.
The latter (proportion of amount redeemed) tends to be the case in the case of extended tie-ins.
You don't want to add the small debt to the big debt for the whole term of the big loan, but you should use the lower interest rate as a lever to help you repay the capital quicker, i.e. you should overpay on the mortgage after you've added the car loan (or whatever it was) to it, so that you pay off the car balance roughly over the same 36-month term as first planned, or at least not too much longer.
You can if you want to, but only if you're foolish enough to decide you want to add the short-term debt to the long-term debt for the whole of the long term, i.e. to spread it as thin as you can. Doing it that way maximises the interst you pay. By paying the capital off more quickly you'll pay less in the long run because less interest is charged.
If you want to calculate the amount of interest you pay when borrowing amount A at rate r per period over n periods, this is equal to:
A * ((nr-1)q + 1)/(q - 1) where q = (1+r)^n
So, for example, if you borrow £5000 at 0.49%pm over 36 months,
first work out q = 1.0049^36 = 1.1924, then work out ((nr-1)q+1)/(q-1) = ((36*0.0049-1)*1.1924+1)/0.1924 which is 0.093233, and finally multiply by £5000 to get £466.17.
An easier way to work out how much it would cost you to add the small loan to the big loan is to work out what proportion the amount you would add to the big loan is of the amount presently outstanding on it. Say you're adding £4500 to a £45000 mortgage balance. That's 10%. If you don't overpay, and let the resulting 110% sum (£49500) decay over the existing mortgage term, your payments will go up by 10% too. So simply multiply your existing mortgage payments by 0.1, and by the number of months left to go, and subtract £4500, and that'll be the total interest you'd pay on this scheme.

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