# Math question

• Dec 20th 2009, 07:58 PM
FuryofLight
Math question
Peter buys a ski vacation package priced at $2754. He pays$350 down and finances the balance at \$147 per month for 1.5 years. Determine the annual interest rate, compounded monthly, being charged.

The only financial question in my text book that i could not solve. Any help would be appreciated. Thanks!
• Dec 20th 2009, 08:23 PM
Krahl
350 was paid straight away so no interest acted upon it.so he needed to pay 2404.
147 for 1.5yrs=18months is 147(18)=2646

so $2404(1+\frac{r}{12})^{12(1.5)}=2646$

solving for r gives you the annual interest rate compounded monthly
• Dec 21st 2009, 06:16 AM
FuryofLight
http://www.mathhelpforum.com/math-he...d7e6a873-1.gif

(1+ r/12)^18=1.1
(1+r/12)= 18 x sq rt of 1.1
r/12= 1.005 -1
r= 0.005 x 12
(am i going the right direction?)

so the interest rate compounded monthly is approximately 6%??

Tvm for the quick reply. =)
• Dec 21st 2009, 07:27 AM
Krahl
• Dec 21st 2009, 07:46 AM
Wilmer
I don't follow/understand what BOTH of you are doing (Doh)

Formula for loan payments:
P = Ai / (1 - k) where k = 1 / (1+i)^n

P = payment (147)
A = amount borrowed (2404)
n = number of months (18)
i = monthly rate (?)

That CANNOT be solved directly: iteration is required.
The rate will be ~12.357% annual, cpd monthly.
All I can say is look up "iteration" or get teacher to demonstrate;
can't teach that here!
• Dec 21st 2009, 09:13 AM
FuryofLight
lol Wilmer, i also had no idea what i was doing, was only following Krahl's equation and solving for 'r' o.o

and yea, Wilmer your answer is correct according to the back of the text book. I just wanted to know if there was another way of solving the question without using 'guess and check'. And I was also told that this question was not even meant for grade 11. >.<
• Dec 21st 2009, 09:46 AM
Krahl
oh yes thanks wilmer. paying monthly you have to remember that 147 is worth more now than it does later.

so

$\frac{147}{(1+r)^{n-1}}+\frac{147}{(1+r)^{n-2}}+...+\frac{147}{(1+r)}=2404$

and you get wilmer's formula