Choose the right factor
The first letter is what you want; the second letter is what you have. Every factor requires a rate per period and a matching number of periods.
Period 0: +$0.00. This is the time-zero cash flow. Periods use the payment interval stated in the model.
| Factor | Value |
|---|---|
| F/P | 1.6105 |
| P/F | 0.6209 |
| F/A | 6.1051 |
| P/A | 3.7908 |
| A/P | 0.2638 |
| A/F | 0.1638 |
The P date is one period before the first A. F occurs with the last A.
Draw N equal amounts at years 1 through N; no amount at year 0.
Cash-flow dates and signs are part of the answer. Model values retain precision; displays round money to cents. Illustrative assumptions exclude taxes and inflation unless stated.
What the model means
F/P and P/F convert a single amount. F/A and P/A convert an ordinary uniform series. A/P is capital recovery; A/F is the sinking-fund factor. They are dimensionless multipliers, although A itself has a per-period meaning.
Build the calculation
For ordinary annuities, P lies one period before the first payment and F coincides with the last. An annuity due begins at the start of each period and gains one extra growth period: multiply the corresponding ordinary-series equivalent by 1+i. At i=0, P/A=F/A=N and A/P=A/F=1/N.
Set up. Calculate. Explain.
Rebuild the starting scenario
Annual amount: 1000 $/year; Interest rate: 10 % per year; Number of years: 5 years. Calculate the present worth of the uniform series.
Setup hint
Draw N equal amounts at years 1 through N; no amount at year 0.
Open the visual solution
- Draw N equal amounts at years 1 through N; no amount at year 0.
- Find P or F with the requested / given factor, not its reciprocal.
- Recover A with A/P or A/F. Sinking fund A/F answers the annual deposit required for a future target.
Period 0: +$0.00. This is the time-zero cash flow. Periods use the payment interval stated in the model.
| Factor | Value |
|---|---|
| F/P | 1.6105 |
| P/F | 0.6209 |
| F/A | 6.1051 |
| P/A | 3.7908 |
| A/P | 0.2638 |
| A/F | 0.1638 |
The P date is one period before the first A. F occurs with the last A.
Draw N equal amounts at years 1 through N; no amount at year 0.
Cash-flow dates and signs are part of the answer. Model values retain precision; displays round money to cents. Illustrative assumptions exclude taxes and inflation unless stated.
Checks allow 0.1% numerical rounding (minimum $0.05 or 0.001 in the stated nonmonetary unit). Interpolated factors and rates are approximations; keep table precision consistent.
Transfer the idea to a new scenario
Receive $2,500 at the end of each of eight years, i=7%. Find present worth.
Setup hint
Draw N equal amounts at years 1 through N; no amount at year 0.
Open the visual solution
- Draw N equal amounts at years 1 through N; no amount at year 0.
- Find P or F with the requested / given factor, not its reciprocal.
- Recover A with A/P or A/F. Sinking fund A/F answers the annual deposit required for a future target.
Period 0: +$0.00. This is the time-zero cash flow. Periods use the payment interval stated in the model.
| Factor | Value |
|---|---|
| F/P | 1.7182 |
| P/F | 0.5820 |
| F/A | 10.2598 |
| P/A | 5.9713 |
| A/P | 0.1675 |
| A/F | 0.0975 |
The P date is one period before the first A. F occurs with the last A.
Draw N equal amounts at years 1 through N; no amount at year 0.
Cash-flow dates and signs are part of the answer. Model values retain precision; displays round money to cents. Illustrative assumptions exclude taxes and inflation unless stated.
Checks allow 0.1% numerical rounding (minimum $0.05 or 0.001 in the stated nonmonetary unit). Interpolated factors and rates are approximations; keep table precision consistent.
To find an annual deposit A that will accumulate to target F, use:
Can you defend your setup?
Can you place each amount on the timeline, match the interest period, calculate the equivalent quantity, and state the decision or limitation?
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