Annual versus quarterly reinvestment
Answer first
With the same $10,000 starting balance and a stated 3% annual yield, one annual reinvestment step ends at $10,300.00. Four equal synthetic quarterly steps end at $10,303.391906640625, a modeled difference of $3.391906640625 (about $3.39). The difference comes from applying each quarter's 0.75% step to the growing balance.
This is arithmetic under explicit assumptions. The quarterly steps are synthetic and do not claim that SCHD pays on that cadence. Actual distributions, eligibility, taxes, prices and broker execution are outside this replay.
Why the two paths differ
The annual path applies 3% once: $10,000 × (1 + 0.03) = $10,300. The synthetic quarterly path applies 0.03 ÷ 4 = 0.0075 four times: $10,000 × (1 + 0.0075)4 = $10,303.391906640625. Both paths use the same initial balance and annual rate; only the modeled step timing changes.
Every intermediate value is downloadable
The table keeps full decimal precision so another reader can recompute each line as previous assets plus the current synthetic dividend. The annual and quarterly rows are deliberately labeled as separate scenarios.
| Scenario | Step | Period | Rate | Modeled dividend | Ending assets |
|---|---|---|---|---|---|
| annual-step | 0 | start | 0.03 | $0.000000 | $10,000.000000 |
| annual-step | 1 | year-end | 0.03 | $300.000000 | $10,300.000000 |
| quarterly-synthetic | 1 | quarter-1 | 0.0075 | $75.000000 | $10,075.000000 |
| quarterly-synthetic | 2 | quarter-2 | 0.0075 | $75.562500 | $10,150.562500 |
| quarterly-synthetic | 3 | quarter-3 | 0.0075 | $76.129219 | $10,226.691719 |
| quarterly-synthetic | 4 | quarter-4 | 0.0075 | $76.700188 | $10,303.391907 |
Zero and boundary tests
At a zero annual rate, both paths return the original $10,000 and the difference is $0.00. At a zero starting balance, both paths remain $0.00 even with a 3% stated rate. These are input boundaries, not observed fund outcomes. The same cases are in the boundary CSV.
Sources and calculation method
The fund context is linked to Schwab Asset Management's SCHD page. The site calculator's growth mechanics are visible in our current calculator source. This page adds a separate, reproducible comparison with clearly labeled assumptions; it does not alter the production calculator.
Formula: annual end = principal × (1 + annual rate); synthetic quarterly end = principal × (1 + annual rate ÷ 4)4. All numbers above are independently recomputed with decimal arithmetic and retained in the downloadable files.
Questions this test can and cannot answer
Does SCHD actually pay four equal quarterly amounts?
No claim is made here. The four equal steps are a modeling device. Use the issuer's dated records for actual payments.
Does the $3.39 difference predict my account?
No. It only follows from this principal, rate, period count and reinvestment assumption. Prices, dates, taxes, fees and eligibility can change an account result.
Can I use the site's main calculator for this comparison?
Use the SCHD dividend calculator for its documented inputs, then keep this synthetic cadence experiment separate from any issuer observation.