The average Scottish family’s debt has shot up by a worrying 21 per cent in the past six months from £6750 last summer to £8190.

The average non-mortgage debt of the UK family is £13,520, up from £9520 in mid-2015 and the highest level for two and a half years, according to Aviva’s latest Family Finance Report, which looks at various types of borrowing including credit cards, store cards, personal loans and overdrafts.

The average credit card debt for Scottish families is £1770, a 17per cent increase on the summer figure of £1510. But there has been a more than fivefold surge in the average overdraft from £480 in the summer to £2970 in the winter.

We might be dealing with mounting debts, but the average family in the UK now saves £105 a month, 50per cent more than the same time five years ago. However, the monthly amount is down on the summer figure of £113.

But is there any point in saving at all?

Many of us would in fact be better off ignoring the urge to save and instead paying off our debts.

Let’s imagine a family has a credit card debt of £2000 and savings of £2000 in an easy access account. The interest rate on the credit card is 19per cent, which means the debt costs £380 a year. But the interest rate on the savings account is a mere 2per cent, so the annual savings interest is just £40. In other words, the family spends more on the debt than it earns on the savings - £340 more to be precise. So, if the family used the money in the savings account to clear the debt, they would be £340 better off a year.

The example assumes the family does not pay tax on the savings. If you add tax into the equation, the savings are even bigger. For example, the 2per cent savings rate drops to 1.6per cent after basic rate tax or 1.2per cent after higher rate tax.

Tax will take a smaller bite out of savings from April 2016, when the Personal Savings Allowance comes into force. We will then no longer pay tax on the first £1000 of interest we earn from savings, or the first £500 if you are a higher rate taxpayer. But you should do the sums, because you could still save by not saving.

The figures are particularly compelling because savings rates are currently so low. The average easy access account pays interest of 1.06per cent, the lowest rate ever recorded, according to Charlotte Nelson at finance expert at Moneyfacts.co.uk, who says: “Anyone looking at the rates available today will perhaps question the benefit of saving at all.”

Anyone with savings who also has costly debts should certainly consider using the cash to clear all or some of their borrowings.

Always pay off the most expensive debts first – and watch out for any penalties. If you have a personal loan, for example, there could be a penalty of several months’ interest if you pay off the debt before the end of the loan term. It can still make financial sense to clear the debt, but you have to factor the penalty into your calculations.

The cheapest - and biggest - debt is usually the mortgage. You should therefore only pay off, or pay down, the mortgage if you have already cleared other, more costly debts. Otherwise, the same calculation applies. So, if the mortgage interest rate is higher than the savings interest rate, you should consider cutting down the amount you owe on the home loan.

The savings can be substantial. Let’s assume you have a £100,000 repayment mortgage at 3.5per cent over 20 years. If you paid just £50 extra a month, you would clear the debt after 18 years and save a total of £4,700.

If it’s cheaper to borrow than to save, there’s nothing to gain by paying off debts. For example, if you have a 0per cent credit card, you are effectively borrowing money for free – until the balance has to be repaid. You should therefore keep any spare cash in a savings account where it can earn interest at a higher rate.

Many experts advise people to keep the equivalent of three months’ earnings in a savings account. But your emergency fund could be costing you dear. Patrick Connolly of?Chase de Vere?Independent Financial Advisers says: “Everybody ideally needs to have an emergency cash fund, which they can access at short notice if required. However, if the amount of interest you’re paying on your debt is more than the rate you’re earning on your savings you are better off using your savings to pay off your debt.”

Let’s go back to our fictitious family. Suppose they used their £2000 savings to clear their debt, but then the boiler broke down. How would they pay for the repair? Well, they could put the bill on the credit card, or possibly take out a loan or overdraft. They wouldn’t be any worse off and would probably have already saved money on the interest payments.

Of course, if you don’t have access to credit, it’s a good idea to keep some money in a savings account in case of an emergency. You should also resist the temptation to get into a debt cycle. So, once you have paid off a debt, don’t then go on a spending spree.

Pensions are the possible exception to the rule that you should clear debts before you start to save. First, there are generous tax breaks on pensions. Second, your employer might contribute to a workplace pension scheme on your behalf. Also, the earlier you start to save into a pension the better. You should therefore only prioritise debt clearance over pension savings if the interest payments on your debts are critically high.