Question

ruths credit card has an apr of 10.91%, and it computes finance charges using the previous balance method on a 30-day billing cycle. during the april billing cycle, she made a $45.17 payment on april 10th and a $88.34 purchase on april 17th. her total at the start of may was $847.64. what was her balance at the beginning of april?
a. $890.91
b. $797.16
c. $796.87
d. $804.47

Explanation:

Step1: Recall the previous balance method formula

The finance charge using the previous balance method is calculated as \( \text{Finance Charge} = \text{Previous Balance} \times \frac{\text{APR}}{365} \times \text{Billing Cycle Days} \). Here, the billing cycle is 30 days, APR is 10.91% or 0.1091. Let the beginning balance of April (previous balance) be \( x \).

Step2: Calculate the finance charge

The finance charge for the 30 - day billing cycle is \( x\times\frac{0.1091}{365}\times30=\ x\times\frac{0.1091\times30}{365}=x\times\frac{3.273}{365}\approx x\times0.008967 \)

Step3: Determine the relationship between May's balance and April's transactions

The balance at the start of May is equal to the previous balance (April's beginning balance) plus the finance charge, minus the payment, plus the purchase. So:
\( 847.64=x + 0.008967x- 45.17+88.34\)
First, simplify the right - hand side:
\(x + 0.008967x-45.17 + 88.34=1.008967x+43.17\)

Step4: Solve for x

Now we have the equation \(1.008967x + 43.17=847.64\)
Subtract 43.17 from both sides:
\(1.008967x=847.64 - 43.17=804.47\)
Then, divide both sides by 1.008967:
\(x=\frac{804.47}{1.008967}\approx797.16\)

Answer:

b. $797.16$