Tanya has a balance of $1700 on a credit card with an apr of 24.2%, compounded monthly. about how much will she save in interest over the course of a year if she transfers her balance to a credit card with an apr of 10.8%, compounded monthly? (assume that tanya will make no payments or new purchases during the year, and ignore any possible late payment fees.)

Balance on credit card = 1700

We use compound interest formula

A =

Where P -> principal amount

r -> rate of interest

t-> years

n - > compounding period (monthly=12)

We consider two cases

Case 1: P= 1700, r=24.2%= 0.242 , t=1 , n= 12

Apply the formula , A =

= 2160.2423

Case 2: P= 1700, r=10.8%= 0.108 , t=1 , n= 12

Apply the formula , A =
= 1892.9664

Amount she saves = 2160.2423 - 1892.9664

= 267.2759

Interest saved = $267.28

i think it's eleven too, don't woosh me here, but according to the "experts" it's 2.

the proof starts from the peano postulates, which define the natural

numbers n. n is the smallest set satisfying these postulates:

  p1.   1 is in n.

  p2.   if x is in n, then its "successor" x' is in n.

  p3.   there is no x such that x' = 1.

  p4.   if x isn't 1, then there is a y in n such that y' = x.

  p5.   if s is a subset of n, 1 is in s, and the implication

      (x in s => x' in s) holds, then s = n.

then you have to define addition recursively:

  def: let a and b be in n. if b = 1, then define a + b = a'

      (using p1 and p2). if b isn't 1, then let c' = b, with c in n

      (using p4), and define a + b = (a + c)'.

then you have to define 2:

  def:   2 = 1'

2 is in n by p1, p2, and the definition of 2.

theorem:   1 + 1 = 2

proof: use the first part of the definition of + with a = b = 1.

      then 1 + 1 = 1' = 2   q.e.d.

note: there is an alternate formulation of the peano postulates which

replaces 1 with 0 in p1, p3, p4, and p5. then you have to change the

definition of addition to this:

  def: let a and b be in n. if b = 0, then define a + b = a.

      if b isn't 0, then let c' = b, with c in n, and define

      a + b = (a + c)'.

you also have to define 1 = 0', and 2 = 1'. then the proof of the

theorem above is a little different:

proof: use the second part of the definition of + first:

      1 + 1 = (1 + 0)'

      now use the first part of the definition of + on the sum in

      parentheses:   1 + 1 = (1)' = 1' = 2   q.e.d.

a sample of water is taken and kept in a beaker in a freezer at a constant temperature of 0°c. if the system is at dynamic equilibrium, which of these statements is true?