A question on mathematics of finance [Simple interest]

[mech-eng]

"Many credit card companies target entering college freshmen with attractive interest rates. What they do not emphasize, however, is that the low rate will be in effect for only a short time, changing automatically to a much higher rate, often in just a few months. Freshman Michael Bronson accepts a credit card offer at %8 annual interest on any
unpaid charges. The rate will increase to 15% annually after 6 months. To furnish his dorm room, he charges a small refrigerator, some bedding, and personal supplies amounting to $457.80. When he receives his first month's bill, he finds that he can pay just a minimum amount of $87.50.
a) If Michael pays the minumum amount and makes no additional charges, how much will he owe the following month.
(answer: 372.77)
b) Suppose Michael continues to pay the same minimum amount for 4 more months. What will he owe at the end of the next month.(answer:26.94)
c) The minumum amount normally is reduced as the total charge is reduced. Suppose each month, the minumum is reduced by $15 and Michael continues to pay only the minumum. can be pay off the charges in 6 months? If not, what will he owe at the
end of 6 months? (answer: no, 166.45)
This from the book Mathematics with Applications by Lial/Hungerford. First of all I cannot understand the parts "at %8 annual interest on any unpaid charges." and "When he receives his first month's bill, he finds that he can pay just a minumum amount of $87.50". What do these parts refer to ? I am not a native English speaker and I do not know
these concepts very well. I have search for the solution on the internet but have found nothing.
My approach for question part a is 457.80-87.50=370.300 but the answer is 372.27

Thank you.

 

[SteamKing]

The money which our hapless freshman charged on the credit card is not free for the first month. Once the charge is accepted, interest starts accruing immediately on the unpaid balance. If our freshman took the time to scan his bill, he would see a separate amount called the 'finance charge' listed in addition to the amount of his charges.

From the OP, it's not clear how the 8% (why did you write %8? A percent sign is not treated like it's currency.) is calculated. Sometimes the year can be 365 days, sometimes 360 days; is the first month 30 days long, 31 days long, or 28 days long? Is the annual interest compounded daily?

 

[pwsnafu]

mech-eng, are you sure this is a simple interest question? It looks like a compound interest question

From the OP, it's not clear how the 8% (why did you write %8? A percent sign is not treated like it's currency.) is calculated. Sometimes the year can be 365 days, sometimes 360 days; is the first month 30 days long, 31 days long, or 28 days long? Is the annual interest compounded daily?

The answer would be no. This is a per-month question.

 

[Borg]

My approach for question part a is 457.80-87.50=370.300 but the answer is 372.27

The $1.97 difference is the interest charge that the credit card company charged that month for loaning the money. This should be calculated by multiplying the amount owed for that month times 8% per year / 12 months. However, the interest charge that I get is $3.05 which would make the balance for the following month $373.35. Are you sure that you have the correct answer for part a?

BTW, I am assuming an interest rate compounded monthly. A daily compounded rate would result in a higher interest charge which would still be more than the $1.97 indicated by your answer.

 

[pwsnafu]

Calculation:

After Payment $457.80 - 87.50 = 370.30$
Interest = $370.30 \times \frac{.08}{12} = 2.47$
Balance = $370.30 + 2.47 = 372.77$
as required.

 

[Borg]

Oops, I didn't notice that his last statement differed from the answer.

It didn't occur to me to calculate the interest after the payment. It's been my experience that if you don't pay off the entire balance, the credit card companies charge interest on the entire balance and not just the portion that hasn't been paid off.

 

[pwsnafu]

It didn't occur to me to calculate the interest after the payment. It's been my experience that if you don't pay off the entire balance, the credit card companies charge interest on the entire balance and not just the portion that hasn't been paid off.

Agree. The textbook is wrong here.

 

[mech-eng]

mech-eng, are you sure this is a simple interest question? It looks like a compound interest question.

Actually, say I do not know it is a simple interest question or not very well. But it is a question from section 5.1
in my 8th edition (Mathematics with applications by Lial/Hungerford) and this section was called as "Simple interest and discount" in the book.

Thank you.