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## geek4me

835 posts

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Topic # 128790 23-Aug-2013 12:12

If you have interest paid monthly into a savings account how is the amount calculated each month?

For example a Bank offers 4% interest calculated daily paid monthly. Is the interest 4% of the daily amount divided by the number of days in a year? If you had \$10,000 at 4% is the calculation \$10,000 x 4% = \$400/365 = \$1.096 so the next day you are getting 10,001.096 x 4% = \$400.043/365 and so on assuming no withdrawals are made. This provides "interest on interest" giving more than the advertised 4% interest per annum. Or, do they reduce the amount of interest paid daily so that the amount paid adds up to exactly \$400 for a whole year?

Are you better of when the interest is calculated daily and paid monthly than a Bank that offers the same interest rate but only pays annually?

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## muppet

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Don't shoot me, but wouldn't you be better off to ask the bank?
Or download the T's and C's for the Account type you have, that should explain it fairly clearly.

## geek4me

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Banks may use different methods so asking one may not be the same for all. Some just say "interest is calculated daily" but do not explain how.

## Byrned

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So on day 1 of the month you have you have \$100. Interest for that day is (\$100*4%)/365, or in this case roughy \$0.011. Day 2 you still only have \$100 so same calculation as above. Day 3 you've put another \$100 in their so the calculation becomes (\$200*4%)/365. Add all of these calculations together over the month, thats how much interest you get paid.

Why is the interest not paid daily? Because then it would be compounding and cost the bank more money.

## TwoSeven

1306 posts

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My guess is the calculation is 10,000 * (0.04/365).  The result would be multiplied by the number of days in the month.

Software Engineer

## geek4me

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Byrned: So on day 1 of the month you have you have \$100. Interest for that day is (\$100*4%)/365, or in this case roughy \$0.011. Day 2 you still only have \$100 so same calculation as above. Day 3 you've put another \$100 in their so the calculation becomes (\$200*4%)/365. Add all of these calculations together over the month, thats how much interest you get paid.

Why is the interest not paid daily? Because then it would be compounding and cost the bank more money.

So the daily interest calculated is not added to your balance till the end of each month and has "interest on interest" from then on rather than daily. This would give less "interest on interest" but still more than 4% pa. I presume Banks that only pay interest annually don't pay any "interest on interest" and it would be exactly 4%.

## JarrodM

824 posts

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geek4me:
Byrned: So on day 1 of the month you have you have \$100. Interest for that day is (\$100*4%)/365, or in this case roughy \$0.011. Day 2 you still only have \$100 so same calculation as above. Day 3 you've put another \$100 in their so the calculation becomes (\$200*4%)/365. Add all of these calculations together over the month, thats how much interest you get paid.

Why is the interest not paid daily? Because then it would be compounding and cost the bank more money.

So the daily interest calculated is not added to your balance till the end of each month and has "interest on interest" from then on rather than daily. This would give less "interest on interest" but still more than 4% pa. I presume Banks that only pay interest annually don't pay any "interest on interest" and it would be exactly 4%.

yep. to work out the effective rate you use this formula:

EAR = (1+r/m)^m-1

where r is the stated rate (4% in this case) and m is the number of compounding periods per year (usually monthly, so 12 usually)

(1+0.04/12)^12-1 = 0.04074154291 -> 4.074%

## geek4me

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JarrodM:
geek4me:
Byrned: So on day 1 of the month you have you have \$100. Interest for that day is (\$100*4%)/365, or in this case roughy \$0.011. Day 2 you still only have \$100 so same calculation as above. Day 3 you've put another \$100 in their so the calculation becomes (\$200*4%)/365. Add all of these calculations together over the month, thats how much interest you get paid.

Why is the interest not paid daily? Because then it would be compounding and cost the bank more money.

So the daily interest calculated is not added to your balance till the end of each month and has "interest on interest" from then on rather than daily. This would give less "interest on interest" but still more than 4% pa. I presume Banks that only pay interest annually don't pay any "interest on interest" and it would be exactly 4%.

yep. to work out the effective rate you use this formula:

EAR = (1+r/m)^m-1

where r is the stated rate (4% in this case) and m is the number of compounding periods per year (usually monthly, so 12 usually)

(1+0.04/12)^12-1 = 0.04074154291 -> 4.074%

Thanks! That makes sense. You get more than the 4% advertised rate and are better of than only getting interest once a year.

## JarrodM

824 posts

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geek4me:
JarrodM:
geek4me:
Byrned: So on day 1 of the month you have you have \$100. Interest for that day is (\$100*4%)/365, or in this case roughy \$0.011. Day 2 you still only have \$100 so same calculation as above. Day 3 you've put another \$100 in their so the calculation becomes (\$200*4%)/365. Add all of these calculations together over the month, thats how much interest you get paid.

Why is the interest not paid daily? Because then it would be compounding and cost the bank more money.

So the daily interest calculated is not added to your balance till the end of each month and has "interest on interest" from then on rather than daily. This would give less "interest on interest" but still more than 4% pa. I presume Banks that only pay interest annually don't pay any "interest on interest" and it would be exactly 4%.

yep. to work out the effective rate you use this formula:

EAR = (1+r/m)^m-1

where r is the stated rate (4% in this case) and m is the number of compounding periods per year (usually monthly, so 12 usually)

(1+0.04/12)^12-1 = 0.04074154291 -> 4.074%

Thanks! That makes sense. You get more than the 4% advertised rate and are better of than only getting interest once a year.

yes, rule of thumb is compound it as frequently as your bank allows.

## sleemanj

1262 posts

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Obligatory XKCD

---
James Sleeman
I sell lots of stuff for electronic enthusiasts...

## geek4me

835 posts

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sleemanj: Obligatory XKCD

If the interest rate is compounded annually it will be \$1,219. If it is compounded monthly it would then be \$1,221.20 :-)

## MaxLV

652 posts

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geek4me: If you have interest paid monthly into a savings account how is the amount calculated each month?

For example a Bank offers 4% interest calculated daily paid monthly. Is the interest 4% of the daily amount divided by the number of days in a year? If you had \$10,000 at 4% is the calculation \$10,000 x 4% = \$400/365 = \$1.096 so the next day you are getting 10,001.096 x 4% = \$400.043/365 and so on assuming no withdrawals are made. This provides "interest on interest" giving more than the advertised 4% interest per annum. Or, do they reduce the amount of interest paid daily so that the amount paid adds up to exactly \$400 for a whole year?

Are you better of when the interest is calculated daily and paid monthly than a Bank that offers the same interest rate but only pays annually?

It's called compound interest.

Compound interest arises when interest is added to the principal of a deposit or loan, so that, from that moment on, the interest that has been added also earns interest. This addition of interest to the principal is called compounding. A bank account, for example, may have its interest compounded every year: in this case, an account with \$1000 initial principal and 20% interest per year would have a balance of \$1200 at the end of the first year, \$1440 at the end of the second year, and so on.

A recent example in the UK.

In the 1928 a person made a donation to the UK government of 500,000 pounds that was to be used to pay off the UK National debt provided certain conditions were met, as those conditions have never been met, that 500,000 pounds has compounded tp 350,000,000 pounds, and Barclays bank is desperate to get rid of it, but they cant. They're looking at the ever increasing interest on interest they have to keep paying this bank account.

http://www.theglobeandmail.com/news/world/huge-donation-awaits-uk-treasury-but-theres-a-hitch/article13828483/

## MaxLV

652 posts

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Byrned: So on day 1 of the month you have you have \$100. Interest for that day is (\$100*4%)/365, or in this case roughy \$0.011. Day 2 you still only have \$100 so same calculation as above. Day 3 you've put another \$100 in their so the calculation becomes (\$200*4%)/365. Add all of these calculations together over the month, thats how much interest you get paid.

Why is the interest not paid daily? Because then it would be compounding and cost the bank more money.

Not how it works.

For interest calculation purposes, the \$0,011 is added to the \$100 on day one, so on day 2 you have \$100.011 plus the interest earned on day 2, on day three it's your \$100 plus the interest from day one, two and three, and so on for each day of the month. That is what it means when the interest is calculated daily and all the interest earned each day is paid once a month into the account.

## geek4me

835 posts

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MaxLV:
Byrned: So on day 1 of the month you have you have \$100. Interest for that day is (\$100*4%)/365, or in this case roughy \$0.011. Day 2 you still only have \$100 so same calculation as above. Day 3 you've put another \$100 in their so the calculation becomes (\$200*4%)/365. Add all of these calculations together over the month, thats how much interest you get paid.

Why is the interest not paid daily? Because then it would be compounding and cost the bank more money.

Not how it works.

For interest calculation purposes, the \$0,011 is added to the \$100 on day one, so on day 2 you have \$100.011 plus the interest earned on day 2, on day three it's your \$100 plus the interest from day one, two and three, and so on for each day of the month. That is what it means when the interest is calculated daily and all the interest earned each day is paid once a month into the account.

So my original post calculation was nearly right. I can imagine ringing a Bank Help Desk and getting a correct explanation would be quite a challenge. "Interest is calculated daily" is as good as it gets .. I thought Geekzone would be a better bet! Thanks for all the helpful comments which have helped me, and hopefully others, better understand how daily interest works.

## TwoSeven

1306 posts

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I was under the impression that the interest was calculated daily on the balance of he account each day, but that it was not added to the account until the end of he month and one would not earn interest on said interest until then.

Software Engineer

## Batman

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Hmm i always thought that to mean i am getting interst every day ... Surely that would make it wayyy mare than 4.07 perecent from the compounding? Perhaps something for fair go :)

Swype on iOS is detrimental to accurate typing. Apologies in advance.

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