Sunday 22 November 2015

Does having lots of bank accounts reduce the amount of interest you get?


I am a bit weird when it comes to bank accounts - I have 64 accounts for my personal affairs alone spread out across 6 banks. Each of the accounts relates to a saving goal (e.g. see below for examples). It's an approach inspired by one of Ramit Sethi's articles.


I like doing it this way because I know exactly how close I am to each of my savings goals and it avoids the mentality of "ooh I have all this money in my account - I can go and splash out!".

However, a friend pointed out that I am perhaps depriving myself of interest by doing it this way. I decided to run the numbers and see if she is correct. In all the below scenarios, I am assuming an interest rate of 3% and that interest is paid monthly.

Scenario 1: 1 bank account with $1000 vs 100 bank accounts with $10 each
Single account:
January: $1000
Feb: $1002.5
March: $1005.01
April: $1007.52
May: $1010.04
June: $1012.57
July: $1015.1
August: $1017.64
Sept: $1020.18
Oct: $1022.73
Nov: $1025.29
Dec: $1027.85
Jan: $1030.42

One hundred accounts (example for one account with balance of $10)
January: $10
Feb: $10.03
March: $10.06
April: $10.09
May: $10.12
June: $10.15
July: $10.18
Aug: $10.21
Sept: $10.24
Oct: $10.27
Nov: $10.30
Dec: $10.33
Jan: $10.36

Verdict: 100 accounts win...or do they?
Due to 2 decimal point rounding, it's actually better to have lots of bank accounts. You actually earn 2.5 cents of interest but it gets rounded up to 3 cents.

Is this true though? I had a look at how rounding operates. In one of my accounts, I had $37.35. Interest rate was 1.5%. That month, I earned 4c of interest. If you do the numbers (37.35 * .015 / 12), I actually should've earnt 4.6 cents of interest, so it should really round up to 5c but they short changed me.

It appears that banks operate on rounding down rather than the nicer kind of rounding that happens at the supermarket.

Scenario 1b: reworked with rounding down
Result:
Single account balance = $1030.36
One hundred accounts cumulative balance = $1024

Verdict
Looks like my friend is right - I am losing out by having lots of accounts. But this example is a little contrived because the vast majority of my accounts have small balances but I have 3 or so accounts (e.g. my emergency fund) where I chuck in a fair bit at a time and would earn better

Scenario 2: $1000 spread out across 100 accounts with 3 main accounts vs 1 account
Details
100 hundred accounts are broken up into 97 accounts with $5 and 3 accounts with $205, $205 and $105 respectively.

Result
Single account balance = $1030.36
One hundred accounts cumulative balance = $1027.12

Verdict
I'm still losing out but ultimately it's like paying $3/year for better financial transparency and a structure that encourages delayed gratification. I'm prepared to pay that price.

Scenario 3 (just for fun): $1 million spread out across 100 accounts with 3 main accounts vs 1 account
Details
100 hundred accounts are broken up into 97 accounts with $5000 and 3 accounts with $205,000 $205,000 and $105,000 respectively.

Result
Single account balance = $1,030,415.89
One hundred accounts cumulative balance = $1,030,410.96

Verdict

I think if you had $1M in cash, you wouldn't be too worried about losing $4.93/year in interest:P


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