# Thread: compound interest problem

1. ## 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 2. 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

thanks in advance!

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

3. 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?

4. 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

5. 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

6. 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.