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The phrase "accumulated account" is correct and usable in written English.
It can be used in contexts where you are referring to a financial account that has gathered or accrued funds over time.
Example: "After several years of saving, I finally checked my accumulated account to see how much I had saved for my vacation."
Alternatives: "accrued balance" or "cumulative account".
Exact(2)
The perpetuation of his tax cuts, the continuation of his new prescription drug benefit, the management of his wars and the interest payments on debt that he accumulated account for a crucial share of the additional sum Obama has amassed.
"For a taxpayer who is under age 62, the accumulated account balance would be converted to an annuity payable at 62, in the form of a 100 percent joint and survivor benefit using the actuarial assumptions that apply to converting between annuities and lump sums under defined benefit plans," it said.
Similar(58)
One inventory in use states that about 700 Mt has been accumulated, accounting for 75% of the primary metal ever produced.
A low amount of CS2 (5.2 μmol/bottle) accumulated, accounting for 1% of the CT + CF transformed.
A similar pattern has been observed in P. falciparum in chromosome 2, in which nonvariable genes (now regarded as genes with low variability as more sequence data has accumulated) accounted for 82% of the genes close to the center of chromosome 2, whereas nearly 75% of the genes located in the subtelomeric regions were polymorphic (Kidgell et al. 2006).
Some of the CO2 produced by respiration of E. coli cells could not be dissolved in the culture broth, and was consequently discharged into the headspace of the flask, where it accumulated on account of insufficient ventilation through the culture plug.
Over the years, you may have accumulated multiple accounts -- 401 k)s from previous employers, IRAs, bank accounts, credits cards.
Until revelations emerged in late 2004 that he had accumulated secret accounts totaling as much as $8 million at Riggs Bank in Washington, the general, who lived spartanly, was rarely accused of corruption himself.
Hard use and accumulating dirt account for many service calls.
For example,if your minimum stock investment is $5,000 and you have just $1,000 in your stock account accumulated from interest, dividends and capital gains - put that $1,000 into your higher interest savings account.
Though you can opt to have it paid monthly, only annual interest can be accumulated in the account itself.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com