UKC

I'm trying to do some homework for work, but I haven't stretched my maths skills for some time and this one has me stumped.
I have a gross amount of £24,000,000, which is 3 years worth of money.
This has taken into account a 10% increase each year.
What is the year 1 amount?

Obviously show your working please, as I need to be able to replicate and explain!

Cheers

In reply to La benya:
24000/(0.9)^3 is the initial amount
wrong
24000/(1+0.1)^3

In reply to La benya:

Assuming you mean 3 years have passed and you want the amount that was there at time zero:

24,000,000 = N x 1.1^3 (N being amount invested, 1.1 being multiplier to increase by 10%, 3 being number of interest cycles)

So: N = 24,000,000/1.1^3 = 18,031,555.2216

In reply to La benya:

x1=1.1*x0
x2=1.1*x1=1.1^2*x0
x3=1.1*x2=1.1^3*x0
x0=x3/1.1^3
=18,000,000

In reply to La benya:

Or perhaps you mean you have £24,000,000 for a 3 year project and need to spread it over that time with a 10% increase in costs each year?

In reply to drysori:
I think this is equivalent to compound interest.

sorry if its not clear
£24,000,000 is the total amount for 3 years profit.
profit has increased 10% each year
what was the year 1 figure.
a+10%=b
b+10%+c
a+b+c=24m

it'll be about £7million

In reply to La benya:

Yes, 7.25 million by my calculation.

In reply to drysori:

Could you explain please? It might stop the steam coming out of my ears!

In reply to La benya:
£24000000/(1+1.1+1.1^2

Year 1 A
Year 2 1.1A
Year 3 1.1^2A

Total A+1.1A+1.1^2A=24000000
A(1+1.1+1.1^2)=24000000
A=24000000/(1+1.1+1.1^2)

In reply to Robert Durran:

Thanks Robert, seems like the correct answer! I don't think i need to go any deeper in explanation than showing the correct formula, so cheers everyone.