Question

A credit card company determines a card​ holder's minimum monthly payment by adding all new interest to​ 1.5% of the outstanding principal. The credit card company charges an interest rate of ​0.05654% per day. On November ​17, a customer used his credit card to pay for the following business​ expenses: van repairs ​($600​), equipment maintenance ​($433​), office supplies ​($66​), and dinner with clients ​($173​). Use the given information and the rule that minimum payments are rounded up to the nearest dollar to answer parts a and b below.

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Part 1
a. Assuming the card holder had no new​ interest, determine his minimum payment due on December​ 1, his billing date.
What is the card​ holder's minimum payment due on December 1

Answer 1

Answer: To calculate the cardholder's minimum payment due on December 1, we need to find the outstanding principal amount. This amount is the sum of the initial balance and the total charges made on November 17.

Given:

Interest rate per day = 0.05654% = 0.0005654 (as a decimal)

Billing date (December 1) to November 17 = 15 days (since there are 15 days between November 17 and December 1)

Step 1: Calculate the total charges made on November 17

Total charges = Van repairs + Equipment maintenance + Office supplies + Dinner with clients

Total charges = $600 + $433 + $66 + $173 = $1272

Step 2: Calculate the outstanding principal on December 1 (without new interest)

Outstanding principal = Initial balance + Total charges

Let's assume the initial balance was $X (unknown).

Outstanding principal = $X + $1272

Step 3: Calculate the new interest accumulated from November 17 to December 1

New interest = Outstanding principal * (Interest rate per day) * (Number of days)

New interest = ($X + $1272) * 0.0005654 * 15

Step 4: Calculate the minimum payment due on December 1

Minimum payment = Outstanding principal + New interest + 1.5% of Outstanding principal

Minimum payment = ($X + $1272) + [($X + $1272) * 0.0005654 * 15] + 0.015 * ($X + $1272)

Now, we need to round up the minimum payment to the nearest dollar. Let's assume the rounded-up minimum payment is $Y.

So, the equation becomes:

$Y = ($X + $1272) + [($X + $1272) * 0.0005654 * 15] + 0.015 * ($X + $1272)

To determine the minimum payment, we would need to know the initial balance $X, which is not provided in the given information. Without this information, we cannot calculate the exact minimum payment due on December 1.