Based on making maximum contributions of £340 a month into a JISA (maximum annual allowance is £4,080) from birth until the age of 18, then £1,270 a month into an adult ISA (the annual allowance is currently £15,240), Alliance Trust Savings calculates the investment could be worth more than £1m by the time they are 42 years and seven months.

Meanwhile if the adult ISA allowance increases to £20,000 in 2017, as announced in the last Budget, today’s newborns could be millionaires by as early as the age of 38.

If they then save until the age of 65, their investment pot could be worth nearly £3m at current contribution levels, or almost £3.75m at the increased £20k limit.

If parents were able to double the maximum JISA contribution and add a further £300 a month into a Child SIPP from birth (so £640 a month) including 20% tax relief, millionaire status could be reached by 36 years and three months at current limits.

Sara Wilson, head of platform proposition at Alliance Trust Savings, said with current low interest rates, money held in cash accounts has less potential for long-term growth than if it is invested in the stockmarket.

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“By investing in the Alliance Trust Junior ISA, by the age of 18 a child could have a pot worth £106,000 at current levels and if contributions continued, by the age of 65, they could have amassed nearly £3 million in ISAs at current limits,” said Wilson. “By investing in SIPPs as well from birth, the combined pot could be worth £5.5 million by age 65 at current limits.”

She said that when deciding where to invest for your child, the impact of fees should be an important consideration as they can have a significant impact on investment growth over the longer term. For instance, investing £340 per month in a Junior ISA via Alliance Trust Savings could build an investment pot worth £2,600 more after 18 years than investing via a percentage fee platform, everything else being equal, simply because of the impact of the platform fees. After 65 years, the ISA investment could be worth £349,000 more with fixed fees – which would make a substantial difference to your child’s income in retirement.