Original Amount

55,500



Form an equation and solve for C.

2C = an expression which describes the way that the money has accumulated over the 3 year period after annual additions and subtractions.

C is the amount at the beginning

(4/3 times C minus 5,000) is the accumulated amount at the end of year 1

[4/3 times (4/3 times C minus 5,000) minus 5,000] is the amount at end year 2

{4/3 times [4/3 times (4/3 times C minus 5,000) minus 5,000] minus 5,000 } is the amount at end year 3 = 2 times C

What does the 4/3 represent ?

The number 4 divided by the number 3.

It's a convenient way off representing an increase of one third.

Solve for C:

2C = {(4/3)x [(4/3)x ((4/3) x C - 5,000) - 5,000] - 5,000 }

I still can't solve it.

Try for one year first. If the man had X dollars, how much do you think he would have after one year?

4/3X - 5000 ??

Yes! Now, how much would he have after two years?

4/3X - 5000 * 4/3X - 5000 ??

Not quite. The X for the second year is the amount after the first year. You have to multiply the amount you have after the first year by 4/3 and then substract 5000. Try to write the equation again.

4/3 - 5000 * 4/3X - 5000 ?

Take the amount after one year (which you calculated) and make that the new X to find the amount in the next year. Don't randomly try to arrange 4/3, X and 5000. Think about what is happening.

Try this. Let's say the amount is $50,000. What is the amount after year one in dollars?

4/3 * 50000 = 200, 000 / 3 = 6666 - 5000 = 1666

You dropped a zero off that division effort, it should be 61,667. Now for step two. How much would he have after two years?

61667 * 4 = 246668 / 3 = 82223 - 5000 = 77223

2C = {(4/3)x [(4/3)x ((4/3) x C - 5,000) - 5,000] - 5,000 }

re-arrange by adding 5000 to both sides of the equation

2C +5000 = (4/3)x [(4/3)x ((4/3) x C - 5,000) - 5,000]

simplify by multiplying both sides of the equation by 3/4

(3/4) x (2C +5000) = [(4/3)x ((4/3) x C - 5,000) - 5,000]

re-arrange by adding 5000 to both sides of the equation

(3/4) x (2C +5000) +5000 = (4/3)x ((4/3) x C - 5,000)

simplify by expanding the terms in brackets using multiplication

(6/4)C +3750 +5000 = (16/9) C - 20,000/3 ( on the next line 8,750 becomes 26250/3)

simplify by collecting like terms (numbers on one side and the unknown C on the other side

(26,250/3) + (20,000/3) = [(16/9) - (6/4)]C = [(32/18) - (27/18)] C = (5/18)C

(46250/3) = (5/18)C

(46250/3)x(18/5) = C

C = 55,500

Good. You see how you are using the formula over and over.

Start with X
After 1 year: X * 4/3 -5000
After 2 years: (X * 4/3 -5000) * 4/3 -5000

See how the value of X in the second year equation is the total value from the first year equation? What will the third year equation look like?

X * 4/3 - 5000 * 4/3 - 5000 * 4/3X - 5000 ?

This will be correct if you add in two sets of parentheses and remove that second X. Can you see where they go? Look at my example.

X * 4/3 - 5000 *( 4/3 - 5000) *( 4/3 - 5000) ?