Time Value of Money
Present/future value, annuities, and discounted cash flow tools for reserve discounting and investment income.
Level payment assumed at $1,000 per period.
| Annuity type | Present value |
|---|---|
| Annuity-immediate (end of period) | 7,722 |
| Annuity-due (start of period) | 8,108 |
| Increasing annuity-immediate (1,2,…,n × $1,000) | 39,374 |
| Level perpetuity-immediate | 20,000 |
Assumptions & limitations
- All time-value calculations assume a level effective interest rate per period and discrete (not continuous) compounding.
- IRR is solved via Newton's method with a bisection fallback; multiple sign changes in a cashflow stream can produce multiple valid IRRs — only one root is returned.
- Duration/convexity treat the first parsed cashflow (time 0) as the initial outlay/price and compute sensitivity on cashflows from period 1 onward.