# compound interest problem

• May 23rd 2007, 12:12 PM
imppy725
compound interest problem
A syntesizer is advertised at $500 down and$100 per month for 18 months. If interest is charged at 18% per annum compounded monthly, what is the cash proce of the synthesizer?

hi guys, i need to know what does $500 down mean and how to calculate it. I know it has something to do with the Annuity formula: A = R[(1+i)^n -1] / i thanks in advance! Michael • May 23rd 2007, 12:18 PM janvdl Quote: Originally Posted by imppy725 A syntesizer is advertised at$500 down and $100 per month for 18 months. If interest is charged at 18% per annum compounded monthly, what is the cash proce of the synthesizer? hi guys, i need to know what does$500 down mean and how to calculate it.

I know it has something to do with the Annuity formula:

A = R[(1+i)^n -1] / i

Michael

I think 500 is discount.

$\displaystyle 1800 = (P - 500)(1 + \frac{18}{1200} )^ \frac{3}{2}$

There now it looks better. :) Solve for P :)

I get P = 21623 :D
• May 23rd 2007, 12:28 PM
imppy725
Quote:

Originally Posted by janvdl
I think 500 is discount.

$\displaystyle A = \frac{(P - 500)(1 + \frac{18}{1200} )^ \frac{3}{2}}{12} + 1800$

Something doesnt look right here. Why are both A and P unknown?

is ur formula the same as mines? if yes, can you plug in numbers u sing my variables, because im getting kind of confused. thanks, and can you tell me how I should be dealing with the discount?
• May 23rd 2007, 12:29 PM
janvdl
Quote:

Originally Posted by imppy725
is ur formula the same as mines? if yes, can you plug in numbers u sing my variables, because im getting kind of confused. thanks, and can you tell me how I should be dealing with the discount?

You'll see i've edited my post :)
• May 23rd 2007, 12:31 PM
imppy725
Quote:

Originally Posted by janvdl
You'll see i've edited my post :)

will you walk me through it please? because i sort of want it in my math language, you know...the stuff i've learnt
• May 23rd 2007, 12:37 PM
janvdl
Quote:

Originally Posted by imppy725
will you walk me through it please?

$\displaystyle 1800 = (P - 500)(1 + \frac{18}{1200} )^ \frac{3}{2}$

In the end you pay 100 for 18 months = 1800. That is A's value.

P is the original price but you got 500 discount. Therefore: (P - 500)

The interest is over 18 months = 1.5 years = $\displaystyle \frac{3}{2}$ years.

But interest is compounded monthly so its 18% x $\displaystyle \frac{1}{12}$

Therefore:
(P - 500) = 1760
P = 2260

Hope it helps. :)