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Preserve the original dates
| Time | Original payment | Base payment | Extra payment |
|---|---|---|---|
| 1 | 200 | 200 | 0 |
| 2 | 200 | 200 | 0 |
| 3 | 700 | 200 | 500 |
| 4 | 200 | 200 | 0 |
Value the two components
At 10% per period, base-annuity PV is 633.9731 and the extra payment’s PV is 375.6574. Their sum is 1,009.6305.
Compare with individual discounting
Discounting 200, 200, 700 and 200 separately gives the same sum. A decomposition is useful only if its amounts and dates reproduce the original cash-flow pattern.
Keep the extra payment on its actual date
Moving the extra 500 to time 4 would create a different stream. Cash-flow additivity permits rearranging the representation, not changing the economic timing.