Let
x--------> the number of sessions
y-------> the total payment
we know that
without membership:
--------> equation
with membership:
--------> equation
using a graph tool------> resolve the system of equations
see the attached figure
the solution is the point
that means
For
the cost is in both forms
so
to justify buying the membership
therefore
<u>the answer is</u>
First step is to get the average daily balance.
Take the sum of each day's balances.
If a payment has been made, the sign will be negative.
From Days 1 - 5 :
Day 1 = $200
Day 2 = $200
...
Day 5 = $200
That's $200 x 5 days = $1000
From Days 6 - 20 :
Day 6 = $350
Day 7 = $350
...
Days 20 = $350
That's $350 x 15 days = $5250
From Days 21 - 30 :
Day 21 = $150
Day 22 = $150
...
Day 30 = $150
That's $150 x 10 days = $1500
A total of :
$1000 + $5250 + $1500 = $7750
Now divide this total to the number of days to get the ADB or Average Daily Balance.
Next Step is to calculate for the finance charge using the formula :
where ADB is the average daily balance
r is the interest rate per day
d is the number of days or period given
From the problem, APR is 15.5%, it means that we need to divide the APR by 365 days.
So r = 0.155/365 = 0.000425
And we have d = 30 days
The charge will be :
Charge = 258.33 x 0.000425 x 30 = $3.29
The answer is $3.29