Examples
Examples
Try the starting example
- Monthly charge (USD)
- 12
- Annual upfront charge (USD)
- 120
- Assumed retained months (1–12)
- 12
- Annual effective discount rate (decimal)
- 0.06
- Monthly cash total (USD)
- $144.00
- Annual cash saving (USD)
- $24.00
- Present value of monthly payments (USD)
- $140.22
- Upfront PV advantage (USD)
- $20.22
Try another scenario
- Monthly charge (USD)
- 12
- Annual upfront charge (USD)
- 120
- Assumed retained months (1–12)
- 8
- Annual effective discount rate (decimal)
- 0.06
- Monthly cash total (USD)
- $96.00
- Annual cash saving (USD)
- -$24.00
- Present value of monthly payments (USD)
- $94.39
- Upfront PV advantage (USD)
- -$25.61
Calculation method
Calculation method
Monthly cash total (USD)
a*c
Annual cash saving (USD)
a*c-b
Present value of monthly payments (USD)
sum(a/(1+d)**(i/12) for i in range(c))
Upfront PV advantage (USD)
sum(a/(1+d)**(i/12) for i in range(c))-b
Symbols and units
- a
- Monthly charge (USD)
- b
- Annual upfront charge (USD)
- c
- Assumed retained months (1–12)
- d
- Annual effective discount rate (decimal)
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Calculation steps and notation
sum(list) adds all entries in the list.
Assumptions & limits
Assumptions & limits
- Monthly payments in advance at months 0 through retained-months−1; annual payment at month 0, no refund. Restrict retained months to 1–12. Supported limits: All numeric inputs must be finite. Only the explicitly described mathematical scenario is supported.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.