Verified answer

Imagine an interest rate of 10% paid annually. 10% of £4000 is £400 so this is the interest you earn in year 1, leaving you with £4400. Next year the interest earned is £440, 10% of £4400, so you have £4840. Basically you are getting "interest on the interest" earned so the net change increases every year provided you make no withdrawal.

It depends entirely on the interest rate and since you have not given any, there is no answer possible. If the interest rate is steady, this is a present value of annuity problem. If the interest rate fluctuates, you may have to make a number of separate calculations. In any case, you need an interest rate. For example, if the interest rate is 8 percent compounded annually, the fund would last almost 21 years. If it earns 6% it would last about 15 years 9 months.

The formula for the value of an annuity is:

V = A/r - A/[r*(1+r)^N)

where:

V = Value (in your case it is £4000)

A is the amount of the payment (in your case it is £400)

r is the periodic interest rate.

N is the number of periods that you get paid.

Unfortunately, you have two unknowns -- N and r

If r = 10% -- then you can get £400 per year forever.

if r > 10%, then the value will actually grow over time.

if r < 10%, then the money will eventually run out. You would need to solve for N