Optimized SQL query when there's no physical connection between tables

Question

I need help with writing more optimized SQL query when there is no logical connection between tables. I wrote some subqueries but I'm not satisfied with it because I'm repeating almost the same subquery twice.
The scheme goes like this:

create table rate (
  rate_date date,
  value decimal(10,2),
  multiplier integer,
  name varchar(3)
  );

create table amount (
  amount decimal(10,2),
  amount_year date,
  rate_name varchar(3)
  );

I want every amount in AMOUNT table to be calculated with multiplier and rate value from RATE table like this amount / multiplier * rate. Common things for both tables are name (some code identifier) and date. Those should be used to get the data together. Only the newest rates for amount_year are taken into account.
You can check this fiddle if you're willing to help. That's my try.

select am.amount / 
    (
      select ra.multiplier 
      from rate ra
      where ra.rate_date = (select max(rate_date) 
                            from rate 
                            where year(rate_date) = year(am.amount_year) and name = am.rate_name) 
        and ra.name = am.rate_name
    ) * (
      select ra.value 
      from rate ra
      where ra.rate_date = (select max(rate_date) 
                            from rate 
                            where year(rate_date) = year(am.amount_year) and name = am.rate_name) 
        and ra.name = am.rate_name
    ) as calculated_amount
    from amount am;

Answer 1

You can use a single subquery to get the newest multipler and value for each year. Then join that with the amount table to do the division.

SELECT am.amount / (r2.multiplier * r2.value) AS calculated_amount
FROM amount AS am
JOIN (SELECT YEAR(rate_date) AS year, MAX(rate_date) AS maxdate
      FROM rate
      GROUP BY year) AS r1 ON YEAR(am.rate_date) = r1.year
JOIN rate AS r2 ON r1.maxdate = r2.rate_date