Regular Saver - Equivalent interest rate by month drops?

schiff

pochisoldi wrote: »

If you want to work out how much you will earn, almost to the penny, you need to make a spreadsheet with twelve rows, one for each monthly payment
In each row you have the following columns
A: The money paid in that month (e.g. £250)
B: The date the money was paid in (e.g. 01/12/18)
C: The date the account matures (e.g. 25/06/19)
The annual interest rate (e.g. 5%) This must be a percentage (i.e. 0.05 or 5% not 5)
E: C-B (= number of days that amount in column A is saved for)
F: =(1+D)^(E/365)-1 (=The interest rate for E days)
G: =A*F (=the interest receivable on that month's payment)

Add up all the amounts in column G, round to 2 decimal places, and that's the approximate figure expect to receive when the account matures.

There was a time when I used to calculate the expected interest on a maturing RS but when it was always only a few pence different, sometimes more, sometimes less, I gave up as it clearly wasn't worth the effort.

I used pen and paper and a calculator and it really didn't take long. eg 3.5%, £250 pm, first deposit 15/4, then monthly on the first WD:

250 15/4 to 30/4 (16 days) (250 x 3.5% divided by 365 x 16) £0.384
500 1/5 to 1/6 (32) £1.534
750 2/6 to 30/6 (29) £2.086
usw

Add the totals. Probably as quick as setting up and loading a spreadsheet.

redux

schiff wrote: »

There was a time when I used to calculate the expected interest on a maturing RS but when it was always only a few pence different, sometimes more, sometimes less, I gave up as it clearly wasn't worth the effort.

[...] Probably as quick as setting up and loading a spreadsheet.

Agreed.

However, even quicker, but still unnecessary, there are simple formulae for calculating sums of certain regular series, without needing to do 12 iterations on a spreadsheet or back of an envelope. In this case it involves a term n(n+1)/2, where n is the number of items, here months, leading to being equivalent to 6.5 months of the headline annual rate on the final amount. Thus for instance £250 a month at 5% earns 6.5/12 x £150, or £81.25 (simple way: half a year, £75, plus half a month, £6.25), which can be worked out in the head without paper or spreadsheet.

That will represent the case when the payments in and maturity are all on the same day of each month. There will be a slight variation if dates are moved around a bit, so opening late in a calendar month then the rest of the payments early makes a bit more.

But I really can't see why anyone would spend several minutes of their time writing and testing a spreadsheet that can produce a hair-splitting exact result that might show for example £3.11 or £2.17 better than the £81.25

Emily_Joy

Perhaps there is quite a lot of overthinking here.

To estimate the interest on the regular saver which allows N deposits of X pounds and has A% AER, I would always use the formula income = 0.05*N*X*A. Usually doesn't require a calculator.

To OP: in order to decide which account to fund first, the simplest way is to find out what income would the amount bring in 24 hours, or in a day. So if you deposit X pounds into an account with A% AER, after 24 hours you it will bring 0.01*A*X/365 pounds.

System

Emily_Joy wrote: »

Perhaps there is quite a lot of overthinking here.

To estimate the interest on the regular saver which allows N deposits of X pounds and has A% AER, I would always use the formula income = 0.05*N*X*A. Usually doesn't require a calculator.

To OP: in order to decide which account to fund first, the simplest way is to find out what income would the amount bring in 24 hours, or in a day. So if you deposit X pounds into an account with A% AER, after 24 hours you it will bring 0.01*A*X/365 pounds.

Is the wrong answer!

RG2015

Emily_Joy wrote: »

Perhaps there is quite a lot of overthinking here.

To estimate the interest on the regular saver which allows N deposits of X pounds and has A% AER, I would always use the formula income = 0.05*N*X*A. Usually doesn't require a calculator.

To OP: in order to decide which account to fund first, the simplest way is to find out what income would the amount bring in 24 hours, or in a day. So if you deposit X pounds into an account with A% AER, after 24 hours you it will bring 0.01*A*X/365 pounds.

Economic wrote: »

Is the wrong answer!

Overthinking indeed!

N * X * A / 200

The second bit looks okay.

Tom99

No formulas or overthinking. 5%pa is more than 3%pa.

Paul_DNAP

Just thinking about the last month's contribution, if you move it over from the 3% to the 5% you will each "11 @ 3% + 1 @ 5%" which is higher than "12 @ 3%"


And whilst is it probably true that the last investment in a regular saver only attracts a tiny return for one month and as much the difference is marginal - it is still better being at a higher rate for that short time, but only a matter of pocket chance, but every 16p counts.

schiff

Tom99 wrote: »

No formulas or overthinking. 5%pa is more than 3%pa.

I wish I had your analytical mind