Failing to understand appeal of regular savers

PinkPig

That's saying that interest is compounded whenever it's paid - or n times a year.

Many regular saver accounts are paid only once a year.

All accounts will quote APR, which is a comparable interest rate independent of how often interest is paid. The APR effectively tells you how much you would earn if interest was paid annually.

Therefore accounts that do pay interest annually will only quote one rate of interest (the APR). Accounts that pay interest monthly will quote a separate rate, lower than the APR, which they use to calculate the monthly interest.

This is all getting very off topic. To reiterate the point of a regular saver, you earn the best available rate on the money you have in it - yes there are limits on how much you can save, but many people would rather have a portion of their savings at 6% rather than none at all.

p00hsticks

Kumquats wrote: »

In essence: using compounding seems like the only way to have a consistent definition of interest rate.

Which is why banks quote the AER (annual equivalent rate) rather than the APR (annual percentage rate) for savings products - it includes any compounding if interest is paid more often than annually

[Deleted User]

Kumquats wrote: »

Okay: here's a more solid example. If you saved $x per year each year over 12 years, you wouldn't think of the interest on the first year's payment as being 12 times the interest on the last year's payment. Even if it was some twelve year account where nothing is "paid" until the end.

I think this sort of thinking should scale: I'm confused why it doesn't.

It doesn't scale because the interest is quoted annually, not 12-yearly. Each year is a separate beast.

Flip_Mode_2016

YorkshireBoy wrote: »

You've misunderstood, yes.

Let's assume you have some income spare each month, say £300. Your choices are either to save this in a Santander 123 account paying 3% AER or in a First Direct account paying 6% AER.

Now, subject to you already having >£3K in Santander, your interest earned will be as follows:

Santander:

(12 x £300) x 3% / 12 x 6.5 = £58.50

First Direct:

(12 x £300) x 6 % / 12 x 6.5 = £117 (so no surprises there!)

Now which is the best account to save the £300 a month in?

Thanks for this info

LXdaddy

Another way to look at the calculation of £300 per month into First Direct earning 6% interest


£300 for 12 months at 6%
£300 for 11 months at 6%
£300 for 10 months at 6%
...
£300 for 1 month at 6%


The first deposit earns interest for 12/12ths of the year and the last deposit earns interest for 1/12th of the year


so we have
£300 * 12/12 *6% +
£300 * 11/12 *6% +
£300 * 10/12 *6% +
...
£300 * 1/12 * 6%


with a bit of rearrangement we get
£300 * (12+11+10+9+8+7+6+5+4+3+2+1)/12 * 6%
which is
£300 * 78/12 *6%
ie £300 * 6.5 *6%




There is no compounding involved in the calculation because interest is only credited to the account at the end of the year and the account is then closed.

Kumquats

LXdaddy wrote: »

...

Someone already wrote this exact argument?

Anyway, my problem with this is that I don't think it's a consistent way to think about interest. I'll post this again because no one has dealt with it:

A thought experiment:

Say we have twelve regular savers: Regular Saver 1, Regular Saver 2, ... Regular Saver 12.

Regular Saver 1 matures at the end of January.
Regular Saver 2 matures at the end of February.
...
Regular Saver 12 matures at the end of December.

Consider the 1st January payment into Regular Saver 1. When Regular Saver 1 matures at the end of January, we put this piece of money, plus the ~1/12 interest we just got paid on it, into Regular Saver 2. And so on, each month. The overall interest we get on this piece of money (plus the interest that we're getting paid each month on this piece of money) is going to be bigger than what it should be, right?

dggar

My 1st. Direct Regular saver has just matured.
I put £300 in for the last 12 months and received £94.10 in interest (after tax at 20%).


So what ever the correct formula is, that is the answer.

YorkshireBoy

dggar wrote: »

My 1st. Direct Regular saver has just matured.
I put £300 in for the last 12 months and received £94.10 in interest (after tax at 20%).


So what ever the correct formula is, that is the answer.

No, that's your answer.

The exact amount returned will depend on the month the account was first funded, and also, depending on whether FD make the SO transfer on a non-working day, the day of the month the payment is scheduled.

LXdaddy

Kumquats wrote: »

Someone already wrote this exact argument?

yes YorkshireBoy wrote a very similar explanation

Anyway, my problem with this is that I don't think it's a consistent way to think about interest.

You may not think it is a consistent way to think about the interest but it is correct. Money which is in the account for 12 months gets a years worth of interest added. Money in the account for 6 months gets half a years worth of interest. Money in the account for one day gets 1/365th (or possibly 1/366th) of a years worth of interest added. None of the interest is added to the account until the end of the year so there is no compounding.

I'll post this again because no one has dealt with it:

A thought experiment:

Say we have twelve regular savers: Regular Saver 1, Regular Saver 2, ... Regular Saver 12.

Regular Saver 1 matures at the end of January.
Regular Saver 2 matures at the end of February.
...
Regular Saver 12 matures at the end of December.

Consider the 1st January payment into Regular Saver 1. When Regular Saver 1 matures at the end of January, we put this piece of money, plus the ~1/12 interest we just got paid on it, into Regular Saver 2. And so on, each month. The overall interest we get on this piece of money (plus the interest that we're getting paid each month on this piece of money) is going to be bigger than what it should be, right?

OK - so if the amount of January's payment will fit into each of the 12 regular savers then yes that particular set of money is compounded - because it spends a month in each account, gets one month's worth of interest added and is then moved to a different account where again it earns a month's worth of interest which is added and it is then moved to the third account etc etc.

So in this theoretical case (if it were possible, as there is a limit to the number of regular savings accounts paying 6% interest that you can hold) the January 1st deposit would gain 6% interest compounded monthly.


£100 deposited on 1st January and cycled through this process would grow to the following at the end of each month (assuming each month is the same length)
£100.50
£101.00
£101.51
£102.02
£102.53
£103.04
£103.55
£104.08
£104.60
£105.12
£105.65
£106.18


That's the result of £100 * (1+(6%/12) ^ 12 ie compounding the interest. The AER of this is probably 6.18%

Ballard

Kumquats wrote: »

Someone already wrote this exact argument?

Anyway, my problem with this is that I don't think it's a consistent way to think about interest. I'll post this again because no one has dealt with it:

A thought experiment:

Say we have twelve regular savers: Regular Saver 1, Regular Saver 2, ... Regular Saver 12.

Regular Saver 1 matures at the end of January.
Regular Saver 2 matures at the end of February.
...
Regular Saver 12 matures at the end of December.

Consider the 1st January payment into Regular Saver 1. When Regular Saver 1 matures at the end of January, we put this piece of money, plus the ~1/12 interest we just got paid on it, into Regular Saver 2. And so on, each month. The overall interest we get on this piece of money (plus the interest that we're getting paid each month on this piece of money) is going to be bigger than what it should be, right?

It is not possible to add the funds or interest from a maturing regular saver into a new one so I'm not sure what you're getting at (or indeed, why).

Let's go through this again...

All regular savers that are currently on the market have a maximum amount that you can pay in each month. You can't add interest paid from elsewhere.

Interest is not paid monthly. It accrues daily and is paid annually.

Bearing in mind these two factors either I don't understand what you're asking or it's not possible. My money is on the latter.