Compound interest question - closing account early

SnowMan

It's not really practicable to attempt this sort of thing because the amounts are so small and it's the competitiveness of the interest rate payable on the account that determines when you need to move money. 

That said it is one argument for choosing annual over monthly interest. And it is also a reason to close accounts when you have moved all/most of the money out especially where there is a significant amount of accrued but unpaid interest at the time the account is emptied but not closed.  

clairec666

Thanks everyone for their input. Definitely not a good money-making scheme, but good for a mathematical discussion.

Rudyson

clairec666 said:

I generally understand how compound interest works, and the difference between gross and AER if interest is paid monthly.

However I'd like some clarification on how interest is calculated if you close an account early.

Example: I have £1000 in an account earning 5%. If I close the account after exactly half a year, I should be paid half of 5%, i.e. £25.
If I put that £1025 into another account also earning 5% I would earn slightly more interest for the second half of the year, because it's being paid on a higher amount.

If you could genuinely gain money this way, surely everyone would be doing it, so is the interest on closure calculated in a different way to remove the benefit of the extra compounding? I.e. not exactly half of 5%?

(This question was posed to me by a very savvy GCSE student and I genuinely didn't know the answer...)

The answer is that you wouldn't receive £1025. The amount would be about £1024.69, which if put into another account at 5% for the remaining 6 months would return £1050.

Ch1ll1Phlakes

clairec666 said:

I generally understand how compound interest works, and the difference between gross and AER if interest is paid monthly.

However I'd like some clarification on how interest is calculated if you close an account early.

Example: I have £1000 in an account earning 5%. If I close the account after exactly half a year, I should be paid half of 5%, i.e. £25.
If I put that £1025 into another account also earning 5% I would earn slightly more interest for the second half of the year, because it's being paid on a higher amount.

If you could genuinely gain money this way, surely everyone would be doing it, so is the interest on closure calculated in a different way to remove the benefit of the extra compounding? I.e. not exactly half of 5%?

(This question was posed to me by a very savvy GCSE student and I genuinely didn't know the answer...)

I understand what your student is trying to do and in theory wthis would work but only if interest paid ANNUALLY. The previous link you mentioned uses an example of £100k which generates at extra £62.50 in a year, which is the equivalent of 0.0625% gain from this method so unless this student is a millionaire (heres hoping) it isn't a worthwhile method and hence why banks don't seem to bothered by it.

clairec666

Rudyson said:

clairec666 said:

I generally understand how compound interest works, and the difference between gross and AER if interest is paid monthly.

However I'd like some clarification on how interest is calculated if you close an account early.

Example: I have £1000 in an account earning 5%. If I close the account after exactly half a year, I should be paid half of 5%, i.e. £25.
If I put that £1025 into another account also earning 5% I would earn slightly more interest for the second half of the year, because it's being paid on a higher amount.

If you could genuinely gain money this way, surely everyone would be doing it, so is the interest on closure calculated in a different way to remove the benefit of the extra compounding? I.e. not exactly half of 5%?

(This question was posed to me by a very savvy GCSE student and I genuinely didn't know the answer...)

The answer is that you wouldn't receive £1025. The amount would be about £1024.69, which if put into another account at 5% for the remaining 6 months would return £1050.

Is this because the bank has adjusted the interest to negate the effect of the extra compounding? I.e. a day's interest is NOT calculated as 1/365 of the year's interest?

Ch1ll1Phlakes said:

clairec666 said:

I generally understand how compound interest works, and the difference between gross and AER if interest is paid monthly.

However I'd like some clarification on how interest is calculated if you close an account early.

Example: I have £1000 in an account earning 5%. If I close the account after exactly half a year, I should be paid half of 5%, i.e. £25.
If I put that £1025 into another account also earning 5% I would earn slightly more interest for the second half of the year, because it's being paid on a higher amount.

If you could genuinely gain money this way, surely everyone would be doing it, so is the interest on closure calculated in a different way to remove the benefit of the extra compounding? I.e. not exactly half of 5%?

(This question was posed to me by a very savvy GCSE student and I genuinely didn't know the answer...)

I understand what your student is trying to do and in theory wthis would work but only if interest paid ANNUALLY. The previous link you mentioned uses an example of £100k which generates at extra £62.50 in a year, which is the equivalent of 0.0625% gain from this method so unless this student is a millionaire (heres hoping) it isn't a worthwhile method and hence why banks don't seem to bothered by it.

He's not a millionaire yet but I can imagine him becoming one in a few year's time, he's exceptionally clever. By which point, he'll have realised his compound interest idea isn't as profitable as he thought....

Ch1ll1Phlakes

Here's an example again for anyone interested using a 5% interest rate and £1000 in funds.

If the interest is paid monthly
That 5% interest rate is the AER and interest would be calculated using the monthly gross rate of 0.4074% (i.e an annual gross rate of 4.889%) and would compound as interest is paid into the account each month.

After 1 month we would have 1000*(1+0.004074) = 1004.07
After 6 months we would have 1000*(1+0.004074)^6 = 1024.69
After 12 months the account has  1000*(1+0.004074)^12 = 1050     which is expected.

If interest is paid annually
The annual gross and AER are equivalent i.e both are 5%. The monthly gross is 1/12 of the annual (it is not paid into the account so it does not compound), that is 5/12% or 0.4167% rounded. The following calculations show what is ACCRUED at each stage but not what is in the account as again the interest is paid annually.

After 1 month we have accrued 1000*(1+0.05*1/12) = 1004.17
After 6 months we have accrued 1000*(1+0.05*6/12) = 1025.00
After 12 months interest is paid and the account has 1000*(1+0.05) = 1050.00  which is again expected.

However, If interest is paid annually and the account is closed after 6 months, reopened, then again closed 6 months later
The interest rates are the same as before (The annual gross and AER are both are 5% and the monthly gross is  0.4167%).

After 6 months the value accrued of £1025 is paid out on closure
Reopening the account and holding for another 6 months gives  1025*(1+0.05*1/2) = £1050.62(5)

So this method does allow for extra interest but on £1000 pound it only generates 62.5p per year or 0.0625%. With so little to gain just having a better interest rate, even 5.1% instead of 5% beats this.

Hope this helps.

nottsphil

Rudyson said:

clairec666 said:

I generally understand how compound interest works, and the difference between gross and AER if interest is paid monthly.

However I'd like some clarification on how interest is calculated if you close an account early.

Example: I have £1000 in an account earning 5%. If I close the account after exactly half a year, I should be paid half of 5%, i.e. £25.
If I put that £1025 into another account also earning 5% I would earn slightly more interest for the second half of the year, because it's being paid on a higher amount.

If you could genuinely gain money this way, surely everyone would be doing it, so is the interest on closure calculated in a different way to remove the benefit of the extra compounding? I.e. not exactly half of 5%?

(This question was posed to me by a very savvy GCSE student and I genuinely didn't know the answer...)

The answer is that you wouldn't receive £1025. The amount would be about £1024.69, which if put into another account at 5% for the remaining 6 months would return £1050.

You have calculated the first six month period as being180 days, presumably to try and demonstrate that there would be no gain. Unfortunately your calculation for the second period also falls short, and the correct answer is that there would be a slight benefit even if only 361 days interest was applied.

SacredStephan

In a 365 day year, you cannot close the account after "exactly half a year", because 365 is an odd number.

You could close it after 182 or 183 days of interest had accrued, assuming the closure day is a banking day.

If there's a 29th Feb during the period when the accounts are open you'd get another day's interest on the balance =366 days.

SacredStephan

clairec666 said:
Is this because the bank has adjusted the interest to negate the effect of the extra compounding? I.e. a day's interest is NOT calculated as 1/365 of the year's interest?

At the point that the interest is calculated the bank won't know about any compounding that might happen in the future. A day's interest IS usually calculated as 1/365 of the gross annual interest.

clairec666

SacredStephan said:

clairec666 said:
Is this because the bank has adjusted the interest to negate the effect of the extra compounding? I.e. a day's interest is NOT calculated as 1/365 of the year's interest?

At the point that the interest is calculated the bank won't know about any compounding that might happen in the future. A day's interest IS usually calculated as 1/365 of the gross annual interest.

That's what I assumed, but it contradicts what Rudyson said