Schwartzman Co., makes a credit card sale to a customer for $800. The credit card sale has a grace period of 30 days and then an interest charge of 1.5% per month is added to the balance. If the unpaid balance on the above sale is $640 at the end of the grace period, the interest charge is

Question

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First, we need to find out how much time has elapsed since the end of the grace period. Let's assume x is the number of months elapsed.

The interest charge is 1.5% per month, so if the unpaid balance is $640, then after x months, the balance will be:

$640 * (1 + 0.015x)

We know that the original sale was $800, and that $160 was paid off during the grace period. Therefore, only the remaining $640 will be subject to interest charges.

Setting the above formula equal to $800 and solving for x:

$640 * (1 + 0.015x) = $800

(1 + 0.015x) = 1.25

0.015x = 0.25

x = 16.67

So 16.67 months have elapsed since the end of the grace period.

Now we can find the interest charge by multiplying the balance at the end of the grace period ($640) by the monthly interest rate (1.5% or 0.015), and then multiplying that by the number of months elapsed (16.67):

$640 * 0.015 * 16.67 = $96

However, we only want the interest charge for the current period (since the end of the grace period), which is the last fraction of a month. We can estimate this by assuming a 30-day month and subtracting the interest for the first 16 full months:

($640 * 0.015 * 16) / 12 = $8

So the interest charge for the current period is:

$96 - $8 = $88

Multiplying this by 0.01 to convert to cents:

$88 * 0.01 = $0.88

Therefore, the interest charge is $0.88, or $9.60 rounded to the nearest cent.

The correct answer is B.