Question

if a mechanic uses his credit card to pay for a compressor that costs $477.95 and does not pay on it until the second month, what will the 1.5% monthly interest charge be at the end of the first month? (1 point) $7.17 $12.83 $18.43 $22.09

Explanation:

Step1: Recall the simple interest formula

The formula for simple interest is $I = P \times r \times t$, where $I$ is the interest, $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. Since the interest is monthly and the rate is given as a monthly rate (1.5% per month), we can adjust the formula for monthly interest. Here, $t = \frac{1}{12}$ years, but since the rate is monthly, we can also use $I = P \times r_{monthly}$, where $r_{monthly}$ is the monthly interest rate in decimal.

First, convert the monthly interest rate from percentage to decimal. The monthly interest rate is 1.5%, so $r = \frac{1.5}{100}= 0.015$.

The principal amount $P = \$477.95$.

Step2: Calculate the interest

Using the formula $I = P \times r$, substitute the values of $P$ and $r$:

$I = 477.95\times0.015$

Calculate the product: $477.95\times0.015 = 7.16925\approx\$7.17$

Answer:

$7.17$ (corresponding to the option \(\boldsymbol{\$7.17}\))