Failing to understand appeal of regular savers

danlightbulb

What do they want?

le_loup

You as a customer to sell you stuff.

Kumquats

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?

Is this really how they calculate interest? I thought interest would be compound, so your money is multiplied by 1.06^{1/12} each month? Doesn't your calculation overestimate the interest?

YorkshireBoy

Kumquats wrote: »

Is this really how they calculate interest? I thought interest would be compound, so your money is multiplied by 1.06^{1/12} each month? Doesn't your calculation overestimate the interest?

My calculation isn't 100% accurate, no, but it's as close as you'll get in one line of formula.

Interest is calculated (and accrues) each day at...

Closing balance x gross p.a. interest rate / 365

(or 366 in a leap year, but lenders don't have to 366!)

But, to your point on compounding, a question for you...

How can the interest compound (monthly, daily, or whenever) when it's not paid until the end of the term? In other words, it's impossible to earn interest on interest (on the FD regular saver being discussed here), since as soon as it's paid the account is closed.

Kumquats

YorkshireBoy wrote: »

My calculation isn't 100% accurate, no, but it's as close as you'll get in one line of formula.

Interest is calculated (and accrues) each day at...

Closing balance x gross p.a. interest rate / 365

(or 366 in a leap year, but lenders don't have to 366!)

But, to your point on compounding, a question for you...

How can the interest compound (monthly, daily, or whenever) when it's not paid until the end of the term? In other words, it's impossible to earn interest on interest (on the FD regular saver being discussed here), since as soon as it's paid the account is closed.

It's an abstraction. I guess I thought it would be calculated by multiplying by 1.06^{1/365} every day, say. It seems very strange to calculate linearly.

Do you have a source from the bank for this calculation? I find it really strange.

I mean, say you had an account that paid 5% APR over 5 years, or whatever time scale, but only "pays" at the end of the term. You'd still expect interest to be calculated compound?

Kumquats

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.

YorkshireBoy

Kumquats wrote: »

It's an abstraction. I guess I thought it would be calculated by multiplying by 1.06^{1/365} every day, say. It seems very strange to calculate linearly.

The opposite is in fact true. I'm only aware of one savings account provider that compounded daily, and that was Egg Banking...years ago.

Do you have a source from the bank for this calculation?

Lots of info on the bba.org.uk website.

I mean, say you had an account that paid 5% APR over 5 years, or whatever time scale, but only "pays" at the end of the term. You'd still expect interest to be calculated compound?

Interest can only compound when it's paid, as I said earlier.

Ballard

Kumquats wrote: »

Do you have a source from the bank for this calculation? I find it really strange.

If you need a second opinion I can confirm that YorkshireBoy's calculation is correct. There are other calculation options for certain products but retail accounts in Sterling are always (to my knowledge) based on a 365 day year.

As has been pointed out, there will be no compounding as the interest is calculated daily but paid annually.

Kumquats

YorkshireBoy wrote: »

The opposite is in fact true. I'm only aware of one savings account provider that compounded daily, and that was Egg Banking...years ago.Lots of info on the bba.org.uk website.Interest can only compound when it's paid, as I said earlier.

Okay, another thought experiment.

Say we have twelve regular savers, so that one matures at the end of each month. Consider the final month's payment into Regular Saver 1, and, after that month, putting this payment and the ~1/12 interest on it into the account maturing the next month, Regular Saver 2. And so on, each month. The APR 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?

Kumquats

Okay, I found a definition on the website you suggested:
I can't post urls, so it's on the bba website under
/policy
/retail
/savings-and-investment
/cash-savings-accounts
/calculation-of-the-annual-equivalent-rate-aer/
But I'm not sure what i is in formula (d): what does "the annual rate to be paid n times a year" mean?

In our case, (alpha = 6%, n=12)
i = (1.06^{1/12} - 1)*100*12

which is closer to the kind of thing I was talking about. But I don't know if i is the object we care about.


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