Two interest calculating questions...

23n1th

Hi Guys,

I'm not math expert but am keeping track of my accounts with a Calc Spreadsheet.

I'm trying to work out the interest I will recieve (profit) on two of my accounts.

Question 1:

How would I work out the returns, interest wise, on a 3.5% 2 years fixed rate isa?

Is it yearly ie: 3.5% of 3600 = 126 (year 1) then 3.5% of 3726 = 134.31 (year 2), or is it calculated at 3.5% of 3600 over the two years (£252)?

Or is it none of the above?

Question 2

I have a children savings account (tax free) at 6% that I pay 100 into a month. Its only allowed £1200 max in it so after a year its transfer out.

Is the interest calculated at the end of the year on the full 1200? Or some arcane calculation taking into account the lower amounts in the account each month up to the 12th month. If so how do I calculate it?

Probably a big ask, cheers.

Lokolo

1) Usually the yearly compounded. Depends on the individual account.

2) Interest is calculated by the average amount in the account over the year/month (whihcever the interest period is). There's a regular saver calculator

http://www.moneysavingexpert.com/savings/best-regular-savings-accounts#calculator

CLAPTON

I'm not sure I would call it 'arcane' calculation

if you borrowed money for a month would you expect to pay interest for a full year?

In the same way, savings are worked out on a daily basis; so the money you paid in on day 1 will earn more interest than the money you paid in the 12th month.
so in your situation

the money you pay in the first month earns
100 x 6%
the money you pay in in the second month earns
100 x 6% x 11/12
the third earn
100 x 6% x10/12
etc

works out as interest =1200 x 6% x 6.5/12

Milarky

'INTEREST' = 'time value of money'

Think SUMPRODUCT(Balance_at_Date_n : Date_Diff(n,n+1))*RATE (if rate is unchanging)

Ilya_Ilyich

Hi 23n1th,

Hope CLAPTON doesn't mind my jumping in! Just to say:
-Using his equation the 6.5 is the 'average' number of months worth of interest each payment gets. The first £100 you pay will get 12 months out of 12 at 6% interest, the next £100 will get 11 months interest, and so on down to 1 month. 6.5 is the average of 12+11+10+...+2+1 so you can then say on average you've made 12 payments of £100 that each on average get 6.5 months of interest at 6% -- so 12 * 100 * 6.5/12 * 0.06 = £39.


The reason this disagrees with the calculator is that it's actually a slightly simplified version of what's going on -- it ignores the effect of compound interest. This doesn't matter a lot in shorter-term calculations (as you can see the difference is pretty small for your case) but the difference can be quite big if you're trying to work out savings over say 5-10 years. To find out the exact numbers is fairly complicated though and you might just want to stick with the calculator or CLAPTON's method; just give a shout if you want to have a try and we try to explain!

Ilya_Ilyich

Generally these accounts work out their compound interest daily but since you're paying every month you can just work it out as compounded monthly. Going to have to go into a little algebra here so I apologise in advance!

Let's say that every month you get paid m% interest -- for the sake of easier sums we'll turn this into a decimal number, so e.g. 1% = 0.01, 5% = 0.05, 1/2% = 0.005 etc.

Say you pay in £100 and leave it for one month -- now you have
100 x (1+m)
so if m was 2%, (1+m) would be 1.02 and after a month you'd have 100 * 1.02 = £102.

If you left it for two months you'd have
100 x (1+m) x (1+m)

Three months would be
100 x (1+m) x (1+m) x (1+m)

...and so on. You can see that if you leave it for 12 months you end up with:
100 x (1+m)^12

(the "^12" just means 12 of them multiplied together)

How does this help us? Well we know that a year's interest = 6% so after a year £100 turns into £106 -- it's been multiplied by 1.06. This must be the same as the formula above (since 12 months' interest = 1 year's interest) so we can say:

100 x 1.06 = 100 x (1+m)^12

This tells us that (1+m)^12 = 1.06. (By this point you really want a spreadsheet to help your sums...)

This is the same as (1+m) = 1.06^(1/12)

What all this gives you is the monthly rate of interest that compounds up to a 6% yearly rate of interest.

To work out how much after one year of saving £100/month you then have....
100 * (1+m)^12
+
100 * (1+m)^11
+
100 * (1+m)^10
+
.....
+
100 * (1+m)^1

You'll pretty much need to plug this into a spreadsheet...add up all the figures and you end up with £1238.65, subtract the £1200 you've paid and you end up with £38.65 interest.

Hope some of this made sense! If you're not using Excel or a similar program you'll find you pretty much need it to do these kind of complex calculations.