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How to work out interest?
oldMcDonald
Posts: 1,945 Forumite
How do you work out interest on a reg. saver account?
If it is 10% and £250 is paid in month 1, then you get the full 10% (minus any tax) on that money? In month 12 you would only get a 12th of the 10% on the last payment? Is that right? I have been trying to work this out for ages and have tied myself up in knots and am now totally confused!
Is there an easy formula to work out interest?
Many thanks
Lisa
If it is 10% and £250 is paid in month 1, then you get the full 10% (minus any tax) on that money? In month 12 you would only get a 12th of the 10% on the last payment? Is that right? I have been trying to work this out for ages and have tied myself up in knots and am now totally confused!
Is there an easy formula to work out interest?
Many thanks
Lisa
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Comments
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You are correct.
£250 * (0.1/12) * 78 = £162.50 (5.4% gross)
£250 your monthly amount
0.1/12 = Monthly Interest
78 is the number of £250 to get the monthly interest,
i.e. at end of month 1, you get the interest on £250, end of month 2, you'd have it on 3(1st months interest, and new interest on £500), until last month you've had it on 78 of them.
Interest is paid annually.0 -
The easy formula is to divide the total amount paid in by 2 and multiply it by the rate (in other words, work it out based on the average balance in the account). This will tend to give you a slight underestimate.
So, for £250/month (£3000 total) at 10%, you would get approximately £150 interest.
If you want the total interest earned on the money when it starts off in a savings account and is transferred into the regular saver, take the average of the two rates and apply it to the total balance. Again, this will be a slight underestimate.0 -
SeanW wrote:You are correct.
£250 * (0.1/12) * 78 = £162.50 (5.4% gross)
£250 your monthly amount
0.1/12 = Monthly Interest
78 is the number of £250 to get the monthly interest,
i.e. at end of month 1, you get the interest on £250, end of month 2, you'd have it on 3(1st months interest, and new interest on £500), until last month you've had it on 78 of them.
Interest is paid annually.
Would you mind explaining more about why you multiply by 78?
Thanks0 -
I was also puzzled by the 78 and wondered if SeanW was calculating net interest assuming tax was levied at 22%. Well it is for a basic rate taxpayer on earned income but I was under the impression that tax was levied at 20% on savings for basic rate taxpayers.0
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No, tax is 20%.
I think it's because he divided by 12 earlier on, he is now multiplying by 78 to get 6.5 overall. I've seen 6.5 in interest calculations before, but I'd like it explained.0 -
78 = 12 + 11 + 10 + ... + 1. Sean's method is based upon the sum of an arithmetic progression. I hadn't seen this before - it's quite nice. It overestimates (due to the assumption that the monthly rate = 1/12 of the annual rate), but it's only over by £2 in this case, whereas mine is under by £10 (because it does not take compounding of interest into account).capehorn wrote:Would you mind explaining more about why you multiply by 78?0 -
78 is 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 +1
which is (12 + 1)*(12/2) (Formula for Arithmetic Series)
i.e., you get 12 months interest on the first £250, and 11 months on the next, ..... until you get only 1 month interest on the last £250
So what I did was work out the monthly interest figure - 10%/12 (which is 0.1/12) = 0.008333333 = 0.833333%.
Then multiply by £250 = £2.08333333
Then multiply by the 78 calculated above
Tax is indeed 20% for basic rate payer, and is to come off the £162.50, Leaving £130, or a total net interest of 4.3%.
As masonic pointed it, this isn't accurate, most banks calculate interest daily. I calculate £163.15 gross total.
I also calculate, that if you were to say have £3000 in the Bradford & Bingley 4.85% AER account, paid annually, and could do an instant transfer into the regular saver every month, you would make a gross interest in total of 7.65%0 -
SeanW wrote:78 is 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 +1
which is (12 + 1)*(12/2) (Formula for Arithmetic Series)
i.e., you get 12 months interest on the first £250, and 11 months on the next, ..... until you get only 1 month interest on the last £250
So what I did was work out the monthly interest figure - 10%/12 (which is 0.1/12) = 0.008333333 = 0.833333%.
Then multiply by £250 = £2.08333333
Then multiply by the 78 calculated above
Tax is indeed 20% for basic rate payer, and is to come off the £162.50, Leaving £130, or a total net interest of 4.3%.
As masonic pointed it, this isn't accurate, most banks calculate interest daily. I calculate £163.15 gross total.
I also calculate, that if you were to say have £3000 in the Bradford & Bingley 4.85% AER account, paid annually, and could do an instant transfer into the regular saver every month, you would make a gross interest in total of 7.65%
*blink*
I would never, ever, ever have worked all that out myself!!
Many thanks to all for your help.
Lisa0 -
Just out of interest, how do you come by that figure? I plugged the following into Excel and came up with £160.13:-SeanW wrote:I calculate £163.15 gross total.Annual Interest = 10% (Decimal multiplier = 1.10) Monthly Interest = 1.1^(1/12) = 1.00797414 -> 0.797414% Month Balance Balance + Interest 1 250.000000 251.993535 2 501.993535 505.996502 3 755.996502 762.024924 4 1012.024924 1020.094953 5 1270.094953 1280.222869 6 1530.222869 1542.425081 7 1792.425081 1806.718130 8 2056.718130 2073.118689 9 2323.118689 2341.643564 10 2591.643564 2612.309694 11 2862.309694 2885.134153 12 3135.134153 3160.134153
The only assumptions I am making with this calculation are that there are equal numbers of days in each month (and that floating point arithmetic can be trusted
). 0 -
I think you are compounding interest, these accounts tend to pay yearly. I am also calculating daily.
Here is my spreadsheet:Yearly Interest 10, Daily 0.00027397260274 = ( (10/100)/SUM(DAYS) ) Month Days Balance Accrued Interest Jan 31 250 2.12328767123288 Feb 28 500 5.95890410958904 Mar 31 750 12.3287671232877 Apr 30 1000 20.5479452054795 May 31 1250 31.1643835616438 Jun 30 1500 43.4931506849315 Jul 31 1750 58.3561643835616 Aug 31 2000 75.3424657534247 Sep 30 2250 93.8356164383562 Oct 31 2500 115.068493150685 Nov 30 2750 137.671232876712 Dec 31 3000 163.150684931507
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