# Calculate the monthly finance charge for the following credit card transaction. Assume that it...

## Question:

Calculate the monthly finance charge for the following credit card transaction.

Assume that it takes 10 days for a payment to be received and recorded and that the month is 30 days long. Assume 365 days in a year. (Round your answer to the nearest cent.)

$3,000 balance, 21% rate,$1,500 payment, adjusted balance method

## Calculating the Monthly Finance Charge:

The adjusted balance method is used to calculate the finance interest for savings accounts. The interest is added to the particular account based on the transaction of the account at every end of the month. The formula is given by:

$$I = Prt$$

Where {eq}P {/eq} is the principal amount, {eq}r {/eq} is the rate of interest and {eq}t {/eq} is time, and {eq}I {/eq} is an interest amount.

## Answer and Explanation:

The payment is {eq}\$1500 {/eq} and the balance amount is {eq}\$ 3000 {/eq}.

The given rate of interest is {eq}21 \% {/eq}.

Now we are going to find the average daily balance:

\begin{align*} P &= \frac{\left( \text{balance} \times 10 \right) + \left( \text{payment} \times 10 \right)}{30} \\[0.3cm] &= \frac{\left( 3000 \times 10 \right) + \left(1500 \times 20 \right)}{30} \\[0.3cm] &= \frac{30000 + 30000}{30} \\[0.3cm] &= \frac{60000}{30} \\[0.3cm] \therefore P &= 2000 \end{align*}

Let us find the monthly finance charge:

\begin{align*} I &= Prt \\[0.3cm] &= 2000 \times \frac{21}{100} \times \frac{30}{365} \\[0.3cm] &= 2000\cdot \frac{6}{73}\cdot \frac{21}{100} \\[0.3cm] &= \frac{252000}{7300} \\[0.3cm] &= \frac{2520}{73} \\[0.3cm] &= 34.52054 \\[0.3cm] \therefore I \ &\approx \ 34.52 \end{align*} \\

Therefore, the monthly finance charge is approximately {eq}\\$ 34.52 {/eq}.