MySQL 8.0

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select version();
Create Table Inflation (Month Date, Rate float);
insert into Inflation values
('2022-06-01', 0.004275),
('2022-05-01', 0.004275),
('2022-04-01', 0.004275),
('2022-03-01', 0.004275),
('2022-02-01', 0.004275),
('2022-01-01', 0.004275),
('2021-12-01', 0.00551667),
('2021-11-01', 0.00551667),
('2021-10-01', 0.00551667),
('2021-09-01', 0.00551667),
('2021-08-01', 0.00551667),
('2021-07-01', 0.00551667),
('2021-06-01', 0.00551667),
('2021-05-01', 0.00551667),
('2021-04-01', 0.00551667),
('2021-03-01', 0.00551667),
('2021-02-01', 0.00551667),
('2021-01-01', 0.00551667),
('2020-12-01', 0.00310833),
('2020-11-01', 0.00310833),
('2020-10-01', 0.00310833),
('2020-09-01', 0.00310833),
('2020-08-01', 0.00310833),
('2020-07-01', 0.00310833),
('2020-06-01', 0.00310833),
('2020-05-01', 0.00310833),
('2020-04-01', 0.00310833),
('2020-03-01', 0.00310833),
('2020-02-01', 0.00310833),
('2020-01-01', 0.00310833),
('2019-12-01', 0.00328333),
('2019-11-01', 0.00328333),
('2019-10-01', 0.00328333),
('2019-09-01', 0.00328333),
('2019-08-01', 0.00328333),
('2019-07-01', 0.00328333),
('2019-06-01', 0.00328333),
('2019-05-01', 0.00328333),
('2019-04-01', 0.00328333),
('2019-03-01', 0.00328333),
('2019-02-01', 0.00328333),
('2019-01-01', 0.00328333);

Select DT.Month, DT.Rate,  EXP(SUM(LOG(1+i2.Rate)))   InfRate 
from (SELECT * FROM `Inflation` WHERE Month between '2020-01-01' and '2022-06-01') as DT
inner join Inflation i2 on DT.Month >=i2.Month
group by DT.Month, DT.Rate
order by Month DESC;

version()
8.0.30

Records: 42  Duplicates: 0  Warnings: 0

Month	Rate	InfRate
2022-06-01	0.004275	1.183162536720466
2022-05-01	0.004275	1.1781260476447084
2022-04-01	0.004275	1.1731109979075227
2022-03-01	0.004275	1.168117296245882
2022-02-01	0.004275	1.1631448517852474
2022-01-01	0.004275	1.1581935740379161
2021-12-01	0.00551667	1.153263372901373
2021-11-01	0.00551667	1.1469361046958126
2021-10-01	0.00551667	1.1406435504366812
2021-09-01	0.00551667	1.1343855196692612
2021-08-01	0.00551667	1.128161822983747
2021-07-01	0.00551667	1.121972272009511
2021-06-01	0.00551667	1.1158166794094042
2021-05-01	0.00551667	1.1096948588740834
2021-04-01	0.00551667	1.1036066251163743
2021-03-01	0.00551667	1.0975517938656625
2021-02-01	0.00551667	1.0915301818623167
2021-01-01	0.00551667	1.0855416068521422
2020-12-01	0.00310833	1.0795858875808637
2020-11-01	0.00310833	1.0762405766329148
2020-10-01	0.00310833	1.0729056317942929
2020-09-01	0.00310833	1.0695810209435526
2020-08-01	0.00310833	1.0662667120587834
2020-07-01	0.00310833	1.0629626732173008
2020-06-01	0.00310833	1.0596688725953394
2020-05-01	0.00310833	1.0563852784677454
2020-04-01	0.00310833	1.0531118592076725
2020-03-01	0.00310833	1.0498485832862758
2020-02-01	0.00310833	1.0465954192724094
2020-01-01	0.00310833	1.0433523358323225