What is this monthly increase payment? Jill has to pay his first payment 1200 USD in January. He also have to pay 1200 USD each month until December, and his payment increases by 1.5%.
I am not sure what this statement means. I will write my calculations below so that you guys can check.
Jan 1200 usd
Feb 1200 × 101.5%
Mar 1200 × 103%
...
And so on
Is my understanding correct?
 A: Note that this answer assumes you are using compound interest, not simple interest.
Unfortunately, you have made a very common mistake when considering compound interest. To understand your mistake, first consider this simple example. On January, I paid $\$100$ to the bank. On each subsequent month, I paid $5\%$ more than I did before. Therefore, each month I multiply the amount I paid last month by $1.05$.
Here are the results:
$$
\begin{align}
& \text{January: $\$1000$} \\
& \text{Febrary: $1000 \times 1.05 = \$1050$} \\
& \text{March: $1050 \times 1.05=\$1102.50$} \\
& \text{April: $1102.50 \times 1.05=\$1157.63$} \\
& \cdots
& \end{align}
$$
If we used your method, then we don't get the right answer. For example, March would be calculated as $1000 \times 1.10 = \$1100$. The error produced by your method becomes more marked as the months go on.
This of course begs the question as to why these two methods produce different answers. The reason is that when you are going from February to March, you are taking $5\%$ of a greater amount. On February, you took $5\%$ of $1000$ and got $\$50$ out. Therefore, on February you pay $\$1050$. So far, so good. However, when we take $5\%$ of $1050$, the following month, we end up with $\$52.50$. Your method assumes that each month, we go up by $50$, when in reality, compound interest means that each month, your money increases by a larger and larger amount. First, $\$50$, then $\$52.50$, and so on.
Can you use these lessons to solve your own problem? If not, then tell me in the comments, and I'll be more happy to do it for you.
