Question

**Advance Algebra With Financial Application**

Sandy purchased a dining room set for $1,140 using a 12-month deferred payment plan with an interest rate of 26.78%. She did not make any payments during the deferment period. What will the total cost of the dining room set be if she must pay off the dining room set within two years after the deferment period?

$1,140.00 <--- My Choice !

Answer 1

A = P(1+r/n)^(n*t)

A = 1140(1+0.2678/12)^(12*1)

So plug that into your calculator and what do you get?

Answer 2

You should get $1,485.70 but that's not the answer

Answer 3

Plug all of this into your calculator

P = 1,485.70((0.2678/12)*(1 + 0.2678/12)^(12*2))/((1 + 0.2678/12)^(12*2) - 1)

After that take the answer you get and multiply it by 24 and that will be your answer

Answer 4

I got .: 1,935.0504

Answer 5

the interest acrrues over the defered time limit:
\[B_1=B_o(1+\frac r{12})^{12}\]
to pay off the balance in 2 years after that would amount to:

\[0=B_1(1+\frac r{12})^2-P\frac{1-(1+\frac r{12})^{24}}{1-(1+\frac r{12})}\]
\[B_1(1+\frac r{12})^2=P\frac{1-(1+\frac r{12})^{24}}{1-(1+\frac r{12})}\]
\[B_1(1+\frac r{12})^2~\frac{1-(1+\frac r{12})}{1-(1+\frac r{12})^{24}}=P\]
\[24*B_1(1+\frac r{12})^2~\frac{1-(1+\frac r{12})}{1-(1+\frac r{12})^{24}}=24*P\]

Answer 6

Omg so confusing ^^

Answer 7

But yes, you're correct so the answer is $1,935.12

Answer 8

i usually try to clean it up with a k=the compounding mess :)

\[24B_1(k)^{24}~\frac{1-k}{1-(1+k)^{24}}=24P\]

Answer 9

i get about 1518 ... but i could be off someplace

Answer 10

1,518 isn't an answer choice the choices are
$1,140.00

$1,485.70

$1,935.12

$2,902.68

Answer 11

@amistre64 :D thank you and @murrcat for the help

Answer 12

you're welcome

Answer 13

lol, then id say its no less than 1518 ;)

Answer 14

i forgot to adjust the begining balance: 36 not 24

Answer 15

now i get 1935

Answer 16

\[24B_1(k)^{36}~\frac{1-k}{1-(1+k)^{24}}=24P~\to~1935\]
yay!!