Netezza SQL how to calculate daily compound interest with varying rates - netezza

Question

I’m having trouble figuring out how to calculate the daily compound interest for an initial amount, over various rates periods, producing a new total that includes the interest amounts from each rate period. The challenge is that for each subsequent rate period you have to calculate the interest on the amount plus the previous interest!!! So it’s not a simple running total.
For example, using the following rates table.
rate from date rate to date rate
-------------- ------------ ----
2013-07-15 2013-09-30 3
2013-10-01 2013-12-31 4
2014-01-01 2014-03-31 3
Using an initial amount of $32,550.37, I have to traverse each rate period with an interest calculation, producing the final amount of $33,337.34.
rate from date rate to date rate daysx amount interest
-------------- ------------ ---- ----- ---------- --------
2013-07-15 2013-09-30 .03 78 32,550.37 209.34
2013-10-01 2013-12-31 .04 92 32,759.71 331.94
2014-01-01 2014-03-31 .03 90 33,091.65 245.69
Final Amount 33,337.34
For example, the initial amount of $32,550.37 has interest of $209.34 at 3%. For the second rate period, I add that interest to the amount, which is $32,759.71 and then calculate the interest on $32,759.71 at 4%. Etc.
I’m using Netezza which does not allow recursive SQL, so I have been trying to use windowed functions, but not with any success yet …
DROP TABLE TRATES;
CREATE TABLE TRATES (RATE_FROM_DATE DATE, RATE_TO_DATE DATE, RATE DECIMAL(10,2));
INSERT INTO TRATES VALUES ('2013-07-15','2013-09-30',.03);
INSERT INTO TRATES VALUES ('2013-10-01','2013-12-31',.04);
INSERT INTO TRATES VALUES ('2014-01-01','2014-03-31',.03);
SELECT TRATES.*
, DAYS_BETWEEN(RATE_FROM_DATE, RATE_TO_DATE)+1 AS DAYSX
, (AMOUNT * POW(1+(RATE)/365,(DAYS_BETWEEN(RATE_FROM_DATE, RATE_TO_DATE)+1)))) – AMOUNT
AS INTEREST
, FIRST_VALUE(AMOUNT) OVER(ORDER BY RATE_FROM_DATE)
*(POW(1+(RATE/100)/365,(DAYS_BETWEEN(RATE_FROM_DATE, RATE_TO_DATE)+1)))
AS NEW_AMOUNT
FROM TRATES
JOIN (SELECT 32550.37 AS AMOUNT) AS TPARMS ON 1=1
;
Any help would be greatly appreciated.

Answer 1

I’m using the fact that the interest rate is shifting is not dependent on which order the shifts occur, so 3 days at 3% followed but 4 days at 2% gives the same result as 4 days at 2% followed by 3 days at 3%.
Furthermore summing logarithms will allow you to multiply over rows:
https://blog.jooq.org/2018/09/21/how-to-write-a-multiplication-aggregate-function-in-sql/
In short: log(a1)+log(a2)+..+log(an) = log(a1*a2*..*an)
This is pretty close to a useful solution (and performs reasonably):
DROP TABLE TRATES if exists;
CREATE temp TABLE TRATES (RATE_FROM_DATE DATE, RATE_TO_DATE DATE, RATE DECIMAL(10,2));
INSERT INTO TRATES VALUES ('2013-07-15','2013-09-30',.03);
INSERT INTO TRATES VALUES ('2013-10-01','2013-12-31',.04);
INSERT INTO TRATES VALUES ('2014-01-01','2014-03-31',.03);
create temp table dates as
select '2010-01-01'::date -1+row_number() over (order by null) as Date
from ( select * from
_v_dual_dslice a cross join _v_dual_dslice b cross join _v_dual_dslice c cross join _v_dual_dslice d
limit 10000 ) x
;
SELECT AMOUNT*pow(10,sum(log(1+rate::double/365)))
FROM TRATES join dates
on date between RATE_FROM_DATE and RATE_TO_DATE
JOIN (SELECT 32550.37 AS AMOUNT) AS TPARMS ON 1=1
group by AMOUNT
I'm sure you can make it prettier with a bit of effort and even let it return the results on select days in the 260 day interval if needed