# Calculating required rate of return for an income-generating savings account

Say someone has £1m.

They want it to generate an increasing level of income, starting from £25k in year 1, and increasing at a rate 7% + inflation pa, such that the end value of the savings after 20 years is £500k nominal.

Assume rate of inflation is 3% over the period.

What is the rate of return required on the account such that the above criteria is met? Line one shows your 1M, a return with a given rate, and year end withdrawal starting at 25,000.

So Line 2 starts with that balance, applies the rate again, and shows the higher withdrawal, by 3%/yr.

In Column one, I show the cumulative effect of the 3% inflation, and the last number in this column is the final balance (903K) but divided by the cumulative inflation.

To summarize - if you simply get the return of inflation, and start by spending just that amount, you'll find that after 20 years, you have half your real value.

The 1.029 is a trial and error method, as I don't know how a finance calculator would handle such a payment flow. I can load the sheet somewhere if you'd like.

Note: This is not exactly what the OP was looking for. If the concept is useful, I'll let it stand. If not, downvotes are welcome and I'll delete.