Geico Corp. moved back into the life insurance business yesterday by signing a letter of intent to purchase Garden State Life Insurance Company of Newark for $10 million.

Geico plans to pay $2.5 million in cash and $7.5 million in debentures paying 15 percent interest for Garden State, which is owned by Motor Club of America Insurance Company, a subsidiary of Motor Club of America.

Since it spun off its Government Employees Life Insurance Co. subsidiary last year, Geico Corp. has not been in the life insurance business. Geico sold its 66 percent share of Gelico to Legal & General Group of the United Kingdom last December for $90 million.

Geico's main operation, Government Employees Insurance Co., collected premiums of $695 million last year primarily from automobile and homeowners insurance.

Spokesman Robert Jackson said Geico expects to sign a definitive agreement to buy all the outstanding share of the New Jersey company as soon as possible.

Garden State Life is licensed to sell insurance in the District of Columbia and 47 states and earned premiums of $2.3 million last year. As of Dec. 31, Garden State had shareholders equity of $11.4 million. Before the company is sold it Geico, it plans to transfer about $5 million of its assets to its parent company.