Thread: Compound Interest

I am having some trouble working out this problem if someone could please explain the steps to solve it.

A dealer advertises that a computer is sold at $450 cash down followed by two yearly installments of $680 and $590 at the end of the first and second year respectively. If the interest charged is 18% per annum compounded annually, find the cash price of the computer.

Let x be the cash price of the computer.
"Cash Down" means you pay off some of the price before compounded interest. Hence the amount of money that is required to pay off the computer becomes x-450

In the first year, if you don't make any more payments at the end of year 0, the debt of (x-450) is interest charged by 18%. In other words, the debt is increased by 18%. Hence the debt becomes 1.18(x-450)

At the end of the first year, we make a payment of $680. Hence our debt is now
what we owe now - what we have paid off
1.18(x-450) - 680 [This is the debt after year 1]

In year 2, the interest is charged again at 18%. Hence our debt now becomes
1.18 [1.18(x-450) - 680]

With a payment of $590 our debt decreases
1.18 [1.18(x-450) - 680] - 590.

If we have fully paid it off, then our debt is equal to 0. Hence
1.18 [1.18(x-450)-680]-590 = 0.

Solve for x.

Thanks for the explanation