I have about £25,000 of premium bonds. If I win I have prize money automatically reinvested in more bonds but lately they have reduced the number of prizes. In past years, on average, I won about £100 a month but since they reduced the prizes, I have won only £50 in three months. I know it is luck, but is it better to keep reinvesting winnings, or withdraw them? — DJ by e-mail

Governments have always been mean with premium bonds but never meaner than now. Bondholders have been forced to share the pain of near-zero interest rates more than most savers.

The average return on premium bonds has been slashed in the past seven months, from a tax-free 3.4% to a wafer-thin 1% a year. That is equal to a building society rate of 1.67% and some building societies pay 2%-3%, so you are definitely making a sacrifice for the remote chance of winning a major prize.

I assume your income and capital growth needs are being met by cash and other orthodox investments. That has to come first.

But, even though the prize pool has been reduced over the past year or so, you still have a far higher chance of winning a prize in premium bonds than winning the National Lottery, plus you can get back your stake back whenever you like.

If you want to do more with your money while still keeping a chance of winning, hold on to the premium bonds but don’t reinvest the prizes. Instead, put the prize money into an emerging market fund. These have higher risks and higher rewards than, say, a FTSE 100 index fund, and will almost certainly be more volatile. But, as Mark Mobius of the Templeton Emerging Market fund pointed out, over the past 18 years the return from this sector has been far higher and the economies of Asia and South America have been less affected by the global credit famine than the major economies of Europe and North America.

As you will be investing irregular amounts over a lengthy period, the volatility will let you buy more when the prices fall. And the risk is far less than from putting back the money into premium bonds. As in any other sector, actively-managed emerging market funds have higher charges than those that automatically follow the shares in an index. One worth looking at is the Lyxor ETF MSCI Emerging Markets GBP (annual cost 0.65%). The Alliance Trust investment dealing service offers a cheap way into that fund, charging a flat £12.50 a deal.

What happens if you mistakenly open two Isas at once? Last year I took out a stocks and shares Isa for £3,600 and then realised I could invest a further £3,600. Because of the banking turmoil I thought it best to take out the second one with a different company but discovered too late that you must put the whole £7,200 with the same provider. It must have been in the small print but I guess I didn’t notice. Is one of them invalid? Should I just hope nobody notices or should I take some sort of action? — PD by email

This is one of those situations where the book says one thing but common sense says another. The trouble is that you cannot rely on being at the mercy of someone with common sense.

The HM Revenue & Customs (HMRC) website is clear: “You are not allowed to invest in more than one stocks and shares Isa, or more than one cash Isa, in the same tax year. If you do this by mistake, the second ISA is invalid and will not qualify for the Isa tax benefits.”

It is not enough simply to close the second Isa. Call the Isa helpline (0845 6041701) and explain the problem. They will advise.

The error should be picked up anyway when the Isa manager of the second plan submits an investor report to the Revenue, as you will have identified yourself by your National Insurance number and the computer will flag the duplication.

However, even the tax people can turn a blind eye on occasion and it seems that in cases like this they usually do.

Jason Butler at Bloomsbury Financial Planning said: “In practice, where the overall amount subscribed to both Isa plans was within the annual limit, it is common for HMRC to write to the investor pointing out the mistake made and the limits that apply, but leaving the second plan open. My advice is to wait for the Revenue to write to you as there is a strong chance that they will let you do that.”

From what you say, you have kept the Isa running into the current tax year without having yet heard from HMRC.

However, while Butler’s advice may be shrewd, bear in mind that the risk is yours. If you come up against an HMRC official who sticks to the rule book, you may have to pay tax that you could have avoided by closing the second Isa and complying with the helpline’s guidance.

It is slightly surprising that the overlap has not already come to light. Maybe one of your Isa providers has not yet reported last year’s new accounts to the authorities.

We are not talking about huge amounts. If you miss out on higher-rate tax relief on dividends worth, say, 5% on £3,600, the loss will be only £72. But the longer the error continues unchecked, the bigger the problem you will accumulate.

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