Updated solution, the do-while was silly ;)

export class G964 {
    public static nbMonths(startPriceOld: number, startPriceNew: number, savingPerMonth: number, percentLossByMonth: number): number[] {
        // start with month 0 and accumulate savings after the first month
        let currentMonth: number = 0;
        let savings: number = 0;

        // we can already check if we have enough capital to buy a new car
        // check if balance is >= 0 after 'selling' the old car + savings and 'buying' a new one
        while ((savings + startPriceOld - startPriceNew) < 0) {
          // update start prices
          let currentPercent = (100-percentLossByMonth) / 100;
          startPriceOld = startPriceOld * currentPercent;
          startPriceNew = startPriceNew * currentPercent;

          // save some money and update percentages
          savings += savingPerMonth;
          percentLossByMonth += (++currentMonth % 2) > 0 ? 0.5 : 0;
        }

        return [currentMonth, Math.round(savings + startPriceOld - startPriceNew)];
    }
}

only works as long as a1.length >= a2.length