Rhodesia's accelerating economic deterioration, rather than purely political or military considerations, explains why Prime Minister Ian Smith is negotiating a peace settlement based on black majority rule with African nationalist leaders.

Stretched to the limit by economic sanctions, world recession and the war's escalating cost, the condition of the economy has become so critical that a prominent business leader said privately he had told Smith. "We cannot go on like this if we want to save anything."

The business community, which opposed Smith's defiant decision to break away from Britain and declare unilateral independence in 1965, now assumes that Rhodesia is surviving on discreet South African financial aid.

Headlines in recent local bank report tell the story succinctly: "Dismal Prospects" for Rhodesia; "Dashed Hopes" for mining; "Faster Decline" for manufacturing, "Bleak Outlook" for money and capital markets, "Further Fall" in construction," "Worst Tourist Year" since the 1950s.

IN 1977 gross domestic product fell for the third successive year - by nearly 7 percent, or the poorest performance since 1945. There was a record number of bankruptcies.

Both white and black unemployment became so serious one industrialist said, "If it was not for the war and both the government and guerrillas recruiting wildly, I don't know what half these guys would be doing."

The Rhodesian dollar has slipped badly against even the declining American currency. Once worth $1.60, the Rhodesian dollar is now traded one for one on the black market.

With white emigration running at a record rate of nearly 11,000 last year, including any draft-age men, Rhodesia may be caught without sufficient white manpower to keep the army or the sophisticated economy going.

White males are still liable for as much as 190 days a year reserve army duty until age 38 - and 70 days until 50. This puts tremendous strain on running an orderly economy.

Contributing to the squeeze on Rhodesia are factors ranging from the war's estimated $900,000-a-day cost to the added expenses of shipping via South Africa now that Mozambique, whose ports are nearer, has closed its border.

Rhodesia could survive the economic sanctions imposed against it if there was no fighting, although they have always meant Rhodesia has sold at a discount and bought at a premium abroad.

Despite disclaimers here, congressional repeal of the Byrd amendment which had allowed American companies to buy Rhodesian chrome last year, hurt Rhodesian badly. It ended a guaranteed source of foreign exchange earnings.

"The Japanese who a few years ago were quite willing in an expanding economy to turn a blind eye to sanctions," a banker said, "now can afford to be moral in obeying them."

There have been numerous bank-ruptcies among one and two-man businesses and some of Rhodesia's biggest companies now are being carried by increasingly worried banks.

Depressed world markets have meant reduced demand for copper, nickel and chrome, for cing ayoffs and mine closings. Also hurt have been agricultural and manufacturing exports.

The South African market, which once absorbed more than 30 percent of Rhodesian manufactured exports, has all but dried up under the effect of a slump there and a 15 percent import surcharge.

Symptomatic of the economy's problems are reported deficits of more than $60 million incured by Rhodesian Railways and more than $10 million by the steel industry.

As the bankreported noted, "Over the past year the damage to the economy has switched from being temporary in character to permanent and structural in nature. . . "

"There is scant comfort to be derived from past successes, the report added, "when so much of what has been achieved in at risk."