Please help, really hard question (1 Viewer)

[waaaaaaaaaam]

Hey, i have been stuck on this question for the last hour, cant seem to get my head around the question

The question is as follows:

Alex pays a deposit on furniture worth $7500, then pays off the balance over 5 years at $180 a month. If the interest rate is a flat 10% p.a., how much deposit did Alex pay?

The answer in the book says $300

My teacher cant figure out answer aswell so help would be greatly appreciated

 

[Drongoski]

Hey, i have been stuck on this question for the last hour, cant seem to get my head around the question

The question is as follows:

Alex pays a deposit on furniture worth $7500, then pays off the balance over 5 years at $180 a month. If the interest rate is a flat 10% p.a., how much deposit did Alex pay?

The answer in the book says $300

My teacher cant figure out answer aswell so help would be greatly appreciated

Let deposit be $D

.: Amount owing is $7500 - $D or $(7500-D)

Since interest rate is FLAT (i.e. not compounding) each yr he has to pay 10% of $(7500-D);
in 5 yrs interest payable is 5 x 10% x (7500 - D)
Alex therefore has to pay off: 1 x (7500-D) + 5x0.1x(7500-D) = 1.5 x (7500-D)

Since there are 5 x 12 = 60 payments of $180 each, total payment is 60 x $180

Therefore: 1.5 x (7500 - D) = 60 x 180

.: 7500 - D = (60 x 180)/1.5 = 7200

.: $D = $300 the deposit paid

 

[waaaaaaaaaam]

Let deposit be $D

.: Amount owing is $7500 - $D or $(7500-D)

Since interest rate is FLAT (i.e. not compounding) each yr he has to pay 10% of $(7500-D);
in 5 yrs interest payable is 5 x 10% x (7500 - D)
Alex therefore has to pay off (7500-D) + 5x0.1x(7500-D) = 1.5 x (7500-D)

Since there are 5 x 12 = 60 payments of $180 each, total payment is 60 x $180

Therefore: 1.5 x (7500 - D) = 60 x 180

.: 7500 - D = (60 x 180)/1.5 = 7200

.: $D = $300 the deposit paid

Thanks man, finally allowed me to cease my troubles
you are genius bro thanks for your help

but one question man
isnt 5x0.1=0.5 not 1.5

 

[Tophel]

but one question man
isnt 5x0.1=0.5 not 1.5

Yes but you're not just paying back the interest, you're also paying back the principal too.

Think of it this way, if the furniture is 7500, that means: Deposit + Balance = 7500

If you can work out the balance then the Deposit will simply be: 7500 - Balance, right?

So what is the Balance? Well you are told that it was all paid off by 60 payments of $180, i.e. $10800. Paying it off means paying back the ACTUAL balance + interest on the balance. Let us assume Balance = $B

So this means:
$B (the actual balance) + $B x 0.1 (interest of 10%) x 5 (5 years) = $10800
$B + 0.5$B = $10800
1.5$B = $10,800
$B = $7,200

Deposit = $7,500 - $7200 = $300

 

[waaaaaaaaaam]

ahh kk
thanks i get it now
thanks for taking the time to help me
cheers, well appreciated