Question

Laura’s credit card has an APR of 12. 04%, and it computes finance charges using the daily balance method and a 30-day billing cycle. On June 1st, Laura had a balance of $606. 40. She made exactly one transaction in June: a payment of $55. 25. If Laura’s finance charge for June was $5. 71, on which day did she make the payment? a. June 8th b. June 12th c. June 15th d. June 20th.

Answer 1

✅ C. June 15th

i got it right on test⬇️

Answer 2

Answer: C. June 15th

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Step-by-step explanation:

Laura starts off with a balance of $606.40

This balance is in effect for x days, where x is some positive whole number between 1 and 30.

For the remaining 30-x days, her balance is 606.40-55.25 = 551.15 dollars after making the payment of $55.25

Here's a table to keep track of everything so far

`\begin{array} \cline{1-3}& A & B\\ \cline{1-3}\text{Interval} & \text{Num Days} & \text{Balance}\\ \cline{1-3}\text{June 1st to June x} & x & 606.40\\ \cline{1-3}\text{June x+1 to June 30th} & 30-x & 551.15\\ \cline{1-3}\end{array}`

where "Num Days" is shorthand for "number of days".

What we do is multiply the A and B column to form column C like this

`\begin{array}c \cline{1-4}& A & B & C\\ \cline{1-4}\text{Interval} & \text{Num Days} & \text{Balance} & \text{A*B}\\ \cline{1-4}\text{June 1st to June x} & x & 606.40 & 606.40x\\ \cline{1-4}\text{June x+1 to June 30th} & 30-x & 551.15 & 551.15(30-x)\\ \cline{1-4}\end{array}`

Add up the stuff in column C

606.40x+551.15(30-x)

Then divide by 30 to compute the average daily balance

`(606.40x+551.15(30-x))/(30)`

That average daily balance is plugged into this formula

`\text{F} = \frac{\text{ADB}*\text{APR}*\text{n}}{365}`

where

• F = finance charge
• ADB = average daily balance
• APR = annual percentage rate
• n = number of days in the billing cycle

We are given the following

• F = 5.71
• APR = 0.1204
• n = 30

Plug in
`\text{ADB} = (606.40x+515.15(30-x))/(30)` and solve for x

So,

`\text{F} = \frac{\text{ADB}*\text{APR}*\text{n}}{365}\\\\5.71 = ((606.40x+551.15(30-x))/(30)*0.1204*30)/(365)\\\\5.71 = ((606.40x+551.15(30-x))*0.1204)/(365)\\\\5.71*365 = (606.40x+551.15(30-x))*0.1204\\\\2,084.15 = 606.40*0.1204x+551.15*0.1204(30-x)\\\\2,084.15 = 73.01056x+66.35846(30-x)\\\\`

`2,084.15 = 73.01056x+1,990.7538-66.35846x\\\\2,084.15 = 6.6521x+1,990.7538\\\\2,084.15-1,990.7538 = 6.6521x\\\\93.3962 = 6.6521x\\\\6.6521x = 93.3962\\\\x = 93.3962/6.6521\\\\x = 14.0401076351829\\\\`

That value is approximate.

When rounding to the nearest whole number, we get x = 14.

Therefore, from June 1st to June 14th, Laura has a balance of $606.40

From June 15th to June 30th, she has a balance of $551.15

The payment was made on June 15th

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Checking the answer:

Here's the updated table with x replaced with 14. So x+1 = 14+1 = 15

`\begin{array} \cline{1-4}& \text{A} & \text{B} & \text{C}\\ \cline{1-4}\text{Interval} & \text{Num Days} & \text{Balance} & \text{A*B}\\ \cline{1-4}\text{June 1st to June 14th} & 14 & 606.40 & 8489.60\\ \cline{1-4}\text{June 15th to June 30th} & 16 & 551.15 & 8818.40\\ \cline{1-4}\end{array}`

Adding everything in column C gets us

8489.60+8818.40 = 17,308

Divide that over 30 days

(17,308)/30 = 576.93

Her average daily balance for the month of June is $576.93

Plug that into the formula mentioned to get the finance charge.

`\text{F} = \frac{\text{ADB}*\text{APR}*\text{n}}{365}\\\\\text{F} = (576.93*0.1204*30)/(365)\\\\\text{F} = (2,083.87116)/(365)\\\\\text{F} = 5.7092\\\\\text{F} = 5.71`

We get the correct finance charge of $5.71, so the answer has been confirmed.