A financial rule of thumb is that households should keep three months' worth of savings on hand in case of an unexpected emergency.

However, holding that cash in the wrong easy access account could prove a costly mistake.

Data from financial site Moneyfacts shows that the worst easy access account on the market pays just 0.01%, yet the average rate on easy access deals has surged 34% in the last three months.

A household earning the national average of £27,000 a year who has the recommended three months’ emergency savings fund of £5,409 would be earning a miserly 54p a year in the worst account.

Those with a bigger cushion of six months’ savings, which for the average worker is £10,820, would get just £1.08.

Here's a look at three better easy access options for your emergency savings fund and how much you could pocket by making the simple switch.

Read more: Your round-up of the top savings accounts

Easy access savings accounts

Your rainy day savings could be earning a much better rate of 1.3% with the RCI Bank Freedom Savings Account.

By moving a pot of £5,409 to this top easy access account, you could earn £70.32 a year.

For those with six months’ stashed away the benefits of switching are even greater.

On a pot of £10,820 moving to the RCI Bank Freedom Savings Account will get you a much better £140.66 after 12 months.

Compare and switch savings accounts today

Easy access Cash ISAs

Savers can now get up to £1,000 worth of savings interest tax-free each year thanks to the Personal Savings Allowance.

But it’s still worth opening an ISA as it will allow you to earn an unlimited amount of interest tax-free, now and in the future when rates get better.

The top easy access Cash ISA deal on the market is the Leeds Building Society Limited Issue Online Access ISA (Issue 3), which pays 1.11%.

On a pot of £5,409 that means pocketing £60 interest a year, while a rainy-day fund of £10,820 will earn £120.

Current accounts

Current accounts that pay in-credit interest are another great home for emergency cash.

At the moment the Santander 123 Current Account is best for larger balances as it pays a flat rate of 1.5% on deposits up to £20,000.

To earn interest, you will need to set up two Direct Debits and deposit at least £500 a month.

The account attracts a £5 monthly fee, but you may be able to offset this cost by earning cashback of up to 3% on your household bills.

On a £5,409 balance, the Santander 123 Current Account would earn you £81.14 a year, while for those with a £10,820 balance that rises to £162.30 (without factoring in the monthly account fee).

Compare current accounts paying in-credit interest

Savings and inflation

Inflation is at a five-year high of 3%. So, ideally, savers need all their money to be earning at least 3% to stop the value of their cash eroding in real terms.

Unfortunately, easy access accounts for large emergency cash reserves are a long way off this sort of rate.

If you are happy to split your money into smaller pots, lock your money away or take on more risk, there are other options available to you.