Calculating APR - Monthly & Weekly

I'm not sure I understand what you are asking.

If you were to calculate weekly repayments and monthly repayments using the same APR, they would add up to a different total amount, because if you pay weekly, you pay the balance off sooner on average so the interest would be calculated on a lower balance. [If you pay monthly, you need to wait until the end of the month before the balance falls, but if you pay weekly then if will fall at weekly intervals over the course of the month]

The quoted APR should not normally change except when the bank makes a decision to alter it.

Most lenders work with monthly repayments and may not be able to accommodate weekly payments except by asking for the monthly amount to be paid earlier. This would increase the actual APR for the loan and it would not be a sensible option.

If you found a lender prepared to do things fairly, a 1000 borrowed at a

10% APR could be repaid with 12 monthly payments of 87.92 or 52 weekly payments of (about) 21.98.

I've used an online calculator for the repayments at

but it is incorrect. It just divides the monthly payment by 4 to get the weekly payment. I suspect the weekly repayment should be closer to 20. Unless someone can find a better calculator for weekly repayments in the next few days, I'll produce something myself.

I make the weekly repayment 20.23.

The above are correct only if the *nominal* rate is 10% per year. The APRs would be 10.47 for the monthly case, and 10.51 for the weekly.

The monthly and weekly repayments with an APR of 10.00 would be £87.72 and £20.18.

I am a nominal kind of person (or, at least, my calculator program is). :)

I would have kept quiet were it not for the fact that DP specifically said "borrowed at 10% APR", which introduced confusion into the proceedings.

Your calculator program is a person? Must be one of those idiot savants.

Agreed. I confess I was a little hesitant about my calculations when every online tool gave 87.92 for the monthly payments. I had assumed, wrongly, that the tools would work with APR's. When I've a spare afternoon, I'll produce a tool to work with APR's.

Why all this obsession with producing tools? A cheap scientific pocket calculator is all you need.

1.1 [start with this as denoting 10% APR] (store memory) (to the power) 12 (reciprocal) (subtract) 1 (equals) [now have the monthly interest rate approx 0.797%] (times) 1000 [for the £1000] (divide) (open bracket) 1 (subtract) (recall memory) (reciprocal) (close bracket) (equals) [now have 87.7155 as required]

For weekly simply replace the 12 with 52.

It's interesting that the above is actually slightly easier than working with nominal rates:

12.1 [start with this as denoting 10% pa nominal, note the trick of adding 12 instead of 1, in preparation for dividing by 12] (divide) 12 (store memory) (subtract) 1 (equals) [now have monthly rate 0.833%] [then as above] (times) 1000 (divide) (open bracket) 1 (subtract) (recall memory) (to the power) (minus) 12 (close bracket) (equals) [now have 87.9159]

For weekly you need to replace *three* instances of 12 with 52.

Of course some minor modifications are necessary for loan periods other than a year. In the APR method, replace the last (reciprocal) with (to the power) (minus) (number of years). In the nominal method, replace the last 12 (or 52) with the actual number of months or weeks in the period.

Some people prefer finding a web page than looking up the formula. If a suitable tool can be readily found, it is usually quicker to find it and use it. I'll post a link a field the criticism (again) when I've produced something. I will, however, admire anyone who takes the calculation back to a formula or first principles.

There are, of course, some people who could use a web page but couldn't use methods like those set out here.

The problem could be more complex than this. In effect the original question is just a different version of the monthly payment, daily accrual, quarterly application system that banks have used since, since......., well quite a long time ago and which we have seen before except this time we have a payment frequency that is not a direct multiple of the accrual period, there not being a whole number of weeks in a month.

This assumes that the OP makes weekly payments but the interest is calculated on a daily basis but applied monthly.

In message , Jclarke writes

It wouldn't alter the advertised APR because that is 'typical'.

It shouldn't alter the contractual APR either so long as the application of interest to the account remains monthly and interest is calculated daily, despite you making weekly payments. If the application of interest were to be weekly as well, which I very much doubt, then the APR would change. The basic APR formula would need to have every '12' replaced by a '52' and would compound 52 times a year instead of 12.

If the interest were calculated on a monthly basis, despite the weekly payments, then so long as the weekly payment were started right away and were in advance then the actual APR would be higher.

I dare say you're right. Sickening, isn't it?

I agree. In my case, a pocket calculator is much easier to find than anything on the bloody web.

Terrible. They should have paid more attention at school.

Mistake: You meant "multiple of the application period". If the accrual period is the day, there *is* a whole number of them both in a week and in a month.

But point taken. Depending on when the payments come in, you could get either 4 or 5 (perhaps exceptionally 3 or 6) payments applied in any one month, which would confuse things a bit.

Not sure why you'd want to assume this. Surely it is getting more and more unusual to apply otherwise than when received. What would be the point in making weekly payments if they're just going to sit around and do nothing until the next monthly application date comes?

Same old question as with the old building society method of making monthly payments but not applying them until year end. Presumably most lenders have mended their ways on this issue by now, no?

I think I was meaning that the interest accrued for a month then was applied.

Most, but not all. B&B for one.