HP12c Credit Card Payment Calculation

[DavidM]

(01-25-2018 05:55 PM)vrenaut74 Wrote:  The answer is below:

Quote:The answer is 11 years. More importantly, how much in interest would you have paid the credit card company?

The answer is $1,902.

You would need to amortize this loan as follows:

Interest on first payment is $30 ($2,000 x 18%) / 12 months
Minimum payment is $54 calculated as the beginning balance ($2,000 x 2.7%)
The principal paid on this payment is $24 (the $54 minimum payment - $30 interest)

For the next payment, the balance is $1,976 ($2,000 - $24) of which $53.35 will paid, broken out at as $29.64 of interest [($1,976 x 18%) / 12] and $23.71 as principal ($53.35 - $29.64). You continue this process to obtain the 11 year answer.

The amortization described above as "the answer" makes perfect sense to me, but the conclusion does not. To gain a better understanding, I put together a table in Excel that rounds the payment and interest amounts to the nearest cent, then determines the principal amount so that the balance can be adjusted properly for the next payment. Accumulated interest is also included for each period.

The first 5 entries of the resulting amortization schedule that results are shown below. As you can see, the first two lines match the above description:

\begin{array}{|crrrrr|}
\hline
\textbf{Pmt #} & \textbf{Balance} & \textbf{Pmt} & \textbf{Int} & \textbf{Principal} & \textbf{Accum. Int} \\
\hline
1 & 2000.00 & 54.00 & 30.00 & 24.00 & 30.00 \\
2 & 1976.00 & 53.35 & 29.64 & 23.71 & 59.64 \\
3 & 1952.29 & 52.71 & 29.28 & 23.43 & 88.92 \\
4 & 1928.86 & 52.08 & 28.93 & 23.15 & 117.85 \\
5 & 1905.71 & 51.45 & 28.59 & 22.86 & 146.44 \\
... & ... & ... & ... & ... & ... \\
\hline
\end{array}

Carrying this through to the 132nd payment (end of 11th year) gives the following results:

\begin{array}{|crrrrr|}
\hline
\textbf{Pmt #} & \textbf{Balance} & \textbf{Pmt} & \textbf{Int} & \textbf{Principal} & \textbf{Accum. Int} \\
\hline
… & … & … & … & … & … \\
128 & 431.64 & 11.65 & 6.47 & 5.18 & 1966.72 \\
129 & 426.46 & 11.51 & 6.40 & 5.11 & 1973.12 \\
130 & 421.35 & 11.38 & 6.32 & 5.06 & 1979.44 \\
131 & 416.29 & 11.24 & 6.24 & 5.00 & 1985.68 \\
132 & 411.29 & 11.10 & 6.17 & 4.93 & 1991.85 \\
\hline
\end{array}

So it doesn't appear that the balance would have been paid off yet at the time indicated in the answer, and the accumulated interest is higher than specified as well. Furthermore, continued payments of 2.7% of the remaining balance will result in a slowly declining balance that eventually stabilizes at $0.55, at which point the 0.01 payment is fully consumed by the interest due. This results in a balance which will never decline from that point forward, so the credit card balance will never be paid off:

\begin{array}{|crrrrr|}
\hline
\textbf{Pmt #} & \textbf{Balance} & \textbf{Pmt} & \textbf{Int} & \textbf{Principal} & \textbf{Accum. Int} \\
\hline
… & … & … & … & … & … \\
676 & 0.57 & 0.02 & 0.01 & 0.01 & 2498.97 \\
677 & 0.56 & 0.02 & 0.01 & 0.01 & 2498.98 \\
678 & 0.55 & 0.01 & 0.01 & 0.00 & 2498.99 \\
679 & 0.55 & 0.01 & 0.01 & 0.00 & 2499.00 \\
680 & 0.55 & 0.01 & 0.01 & 0.00 & 2499.01 \\
… & … & … & … & … & … \\
\hline
\end{array}

It seems to me that one of the following must be true:

- I am making some huge errors in my interpretation of this problem, or at the very least my implementation of the solution
- There are unstated assumptions or qualifications for the problem that have yet to be disclosed (eg. minimum payment "no less than" some amount)
- The stated answer from the course administrator is in error

I'd be most grateful if someone could clarify what circumstances would make the course administrator's solution match the stated outcome of an 11-year payoff with accumulated interest of $1902. The closest I've come is if I set a minimum payment of 2.7% or $21, whichever is greater.

Has anyone else been able to confirm the administrator's result? I'd appreciate seeing more details about how this problem is supposed to be solved.