how does compound interest work -say you have £4000?

Question

how long will it last in the bank if you withdraw £400 every year considering interest rate fluctuation?

Answer 1

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.

Answer 2

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.

Answer 3

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