The question seems trivial at first, but I have problems wrapping my head around this.
Consider a business that starts on day 0 with 1000 customers each paying 6 dollar for 6 months in advance. There are no partial payments or anything. The payment interval stays the same fixed to 6 months. Now, every day, the business gains 3 more customers, each paying 6 dollar for 6 months. After 6 months, the initial 1000 customers pay again their 6 dollar for the following interval. The day after, there are 3 recurring payments plus 3 new payments and so on.
The question is: How much money does the business have on hand on a given day x?
Let's assume for simplicity, that 6 months = 180 days. Some calculations:
Day 0: 1000 * 6$ Day 1: (1000 + 3*1) * 6$ Day 100: (1000 + 3*100) * 6$ Day 180: (1000*2 + 3*180) * 6$ Day 181: (1000*2 + 3*181 + 3*1) * 6$
Can someone help me figuring out the formula to calculate the money available on a given day X?