How can I aim to turn an empty ISA into £275k by buying cheap shares this summer

I can't wait to start putting in this year's ISA and now seems like a good time to do it as I see cheap shares everywhere I look.

They got that a little cheaper last week, with FTSE 100 down 1.18% to close at 8,155.72 on Friday. That makes me want to buy more.

I won't be able to top up my full £20k Stocks and Dividends ISA this year. However, I will invest as much as possible. Given time, I think it's possible for me to go from scratch to saving a large sum, something like £275,000. That would make my retirement look pretty sweet.

FTSE 100 buying spree

I won't put a penny into a Cash ISA. I have a savings account for easy access for short-term emergencies, but stocks are the best way I know to build long-term wealth. While you may be getting 5% on cash today, that will drop if the Bank of England lowers interest rates.

In contrast, these two FTSE 100 stocks pay an average income of 7% and with luck, may continue to do so whatever happens to the underlying values.

FTSE 100 a mining giant Rio Tinto (LSE: RIO) looks really cheap, trading at just 8.8 times earnings. That is below the FTSE 100 average of 12.7 times.

It has a trailing dividend yield of 6.9% per annum, covering a respectable 1.7 times in earnings. It is predicted that next year it will produce 6.9%.

Assignments are not guaranteed. As this table shows, Rio Tinto's board has cut shareholder payouts recently.

Chart with TradingView

Like all mining stocks, Rio Tinto has been hit by the economic slowdown in China. Revenue reached $63.5bn in 2021 but fell to $55.6bn in 2022 and $54bn in 2023.

Sales are forecast to further decline to $53.1bn in 2024 and $53.7bn in 2025. So there is a reason why it is cheap.

Stocks of great value

Rio Tinto's share price has fallen 6.54% in the past week and is down 3.53% in one year. Yet from a long-term perspective, today's low valuation provides an excellent entry price. I will buy it as soon as I have the cash, then sit tight and wait for recovery.

Now, let's say I had £10k to invest in my ISA this tax year and put £5k in Rio Tinto and £5k in FTSE 100 insurance. Avivawhich is forecast to yield 7.2%.

Combined, that would give me an average yield of 7.05%. On a £10k stake, I would earn £705 in the first year.

If these stocks deliver an average total return of 7% per annum it will take me 49 years to hit my £250k target. That's too far.

However, if I put another £10k into an ISA every year I will get there in just over 14 years. And if my stock picks are right and deliver a 9% annualized total return, I'll get there in less than eight years. Of course, there is a risk that it won't happen and I could lose money. But that's my strategy and I'll be following it over the summer, by filling my ISA with cheap UK shares.