The graph of the bank account balance over the sixteen days.
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The balance will increase when the inflow rate is higher than the outflow rate, and it
will decrease when the outflow rate is higher than the inflow rate.
The net flow rate is the difference between the inflow rate and the outflow rate at
any given moment.
If the net flow rate is positive, the balance increases. If the net flow rate is negative,
the balance decreases.
Start with the initial balance of $100.
( t = 0 \) with a balance of $100.
For each segment, the net flow rate (inflow rate - outflow rate).
Starting from $100, plot the balance by accumulating the net changes over time.
Assume the graph shows the following inflow and outflow rates over four time segments:
- Days 0-4: Inflow = 10/day, Outflow = 5/day
- Days 4-8: Inflow = 4/day, Outflow = 6/day
- Days 8-12: Inflow = 7/day, Outflow = 3/day
- Days 12-16: Inflow = 5/day, Outflow = 5/day
Calculations
1. Days 0-4:
- Net flow rate = 10 - 5 = +5/day
- Balance increases by 5/day for 4 days.
- Change in balance = 5/day * 4 days = +20
- New balance at day 4 = 100 + 20 = 120
2. Days 4-8:
- Net flow rate = 4 - 6 = -2/day
- Balance decreases by 2/day for 4 days.
- Change in balance = -2/day * 4 days = -8
- New balance at day 8 = 120 - 8 = 112
3. Days 8-12:
- Net flow rate = 7 - 3 = +4/day
- Balance increases by 4/day for 4 days.
- Change in balance = 4/day * 4 days = +16
- New balance at day 12 = 112 + 16 = 128
4. Days 12-16:
- Net flow rate = 5 - 5 = 0/day
- Balance remains constant.
- New balance at day 16 = 128