Exhibit 99.1

NEWS RELEASE

FOR IMMEDIATE RELEASE

CENTURY BANCORP, INC. ANNOUNCES RECORD EARNINGS OF $36.2 MM FOR 2018, CORE

EARNINGS UP 17.8%; ASSET GROWTH TO RECORD $5.2 BB; REGULAR DIVIDEND DECLARED

Medford, MA, January 15, 2019 — Century Bancorp, Inc. (NASDAQ:CNBKA) (www.centurybank.com) (“the Company”) today announced net income of $36.2 million for the year ended December 31, 2018, or $6.50 per Class A share diluted, an increase of 62.4% compared to net income of $22.3 million, or $4.01 per Class A share diluted, for the same period a year ago. The Company’s core earnings⁽¹⁾ increased by $5.5 million or 17.8% from $30.7 million in 2017 to a record $36.2 million in 2018.

On December 22, 2017, the Tax Cuts and Jobs Act (the “Tax Act”) was enacted, which lowered the Company’s federal tax rate from 34% to 21%. As a result of the rate reduction, the Company recorded a reduction in the value of its net deferred tax asset resulting in a charge of $8.4 million to 2017 income tax expense. This $8.4 million charge is excluded from core earnings.

Total assets increased 7.9% from $4.79 billion at December 31, 2017 to $5.16 billion at December 31, 2018. For the quarter ended December 31, 2018, net income totaled $9.9 million or $1.78 per Class A share diluted, compared to $25,000, or $0.00 per Class A share diluted, for the same period a year ago.

Net interest income totaled $92.6 million for the year ended December 31, 2018 compared to $85.6 million for the same period in 2017. The 8.1% increase in net interest income for the period is primarily due to an increase in average earning assets. The net interest margin decreased from 2.25% on a fully taxable equivalent basis in 2017 to 2.18% for the same period in 2018. This was primarily the result of a decrease in the federal corporate tax rate from 34% to 21% as well as lower prepayment penalties collected during 2018. The decrease in the tax rate results in a lower tax equivalent yield on tax-exempt assets. The average balances of earning assets increased by 5.1% combined with an average yield increase of 0.26%, resulting in an increase in interest income of $23.6 million. The average balance of interest bearing liabilities increased 3.7% combined with an average yield increase of 0.41%, resulting in an increase in interest expense of $16.7 million.

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The provision for loan losses decreased by $440,000 from $1,790,000 for the year ended December 31, 2017 to $1,350,000 for the same period in 2018, primarily as a result of net recoveries of $938,000 offset by changes in qualitative factors.

The Company’s effective tax rate decreased from 32.9% for 2017 to 4.2% for the same period in 2018. This was primarily as a result of a reduction in the value of its net deferred tax asset resulting in a charge of $8.4 million to 2017 income tax expense as a result of the Tax Act as previously discussed. Also, the federal tax rate decreased from 34% to 21% as a result of the Tax Act, offset somewhat by an increase in taxable income.

At December 31, 2018, total equity was $300.4 million compared to $260.3 million at December 31, 2017. The Company’s equity increased primarily as a result of earnings, offset somewhat by dividends paid.

The Company’s leverage ratio stood at 6.91% at December 31, 2018, compared to 6.78% at December 31, 2017. The increase in the leverage ratio was due to an increase in stockholders’ equity, offset somewhat by an increase in quarterly average assets. Book value as of December 31, 2018 was $53.96 per share compared to $46.75 at December 31, 2017.

The Company’s allowance for loan losses was $28.5 million or 1.25% of loans outstanding at December 31, 2018, compared to $26.3 million or 1.21% of loans outstanding at December 31, 2017. The ratio of the allowance for loan losses to loans outstanding has increased, primarily as a result of changes in qualitative factors related to general economic factors pertaining to certain industries. Non-performing assets totaled $3.5 million at December 31, 2018, compared to $1.7 million at December 31, 2017. Nonperforming assets increased mainly as a result of one residential real estate property classified as other real estate owned.

The Company’s Board of Directors voted a regular quarterly dividend of 12.00 cents ($0.12) per share on the Company’s Class A common stock, and 6.00 cents ($0.06) per share on the Company’s Class B common stock. The dividends were declared payable February 15, 2019 to stockholders of record on February 1, 2019.

The Company, through its subsidiary bank, Century Bank and Trust Company, a state chartered full service commercial bank, operating twenty-seven full-service branches in the Greater Boston area, offers a full range of Business, Personal and Institutional Services.

Century Bank and Trust Company is a member of the FDIC and is an Equal Housing Lender.

This press release contains certain “forward-looking statements” with respect to the financial condition, results of operations and business of the Company. Actual results may differ from those contemplated by these statements. The Company wishes to caution readers not to place undue reliance on any forward-looking statements. The Company disclaims any intent or obligation to update publicly any such forward-looking statements, whether in response to new information, future events or otherwise.

Century Bancorp, Inc. and Subsidiaries

Consolidated Comparative Statements of Condition (unaudited)

(in thousands)

Century Bancorp, Inc. and Subsidiaries

Consolidated Comparative Statements of Income (unaudited)

For the quarter and year ended December 31, 2018 and 2017

(in thousands)

Century Bancorp, Inc. and Subsidiaries

Consolidated Year-to-Date Average Comparative Statements of Condition (unaudited)

(in thousands)

Century Bancorp, Inc. and Subsidiaries

Consolidated Selected Key Financial Information (unaudited)

(in thousands, except share data)