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Interest rates and savings have positive correlation. Savings increase as interest rates increase and vice versa.
The third pillar is investments. Since savings are available as loans which are invested by firms, interest rate is readjusted on the principles of demand and supply.
As interest rate rise, so do savings, if there is no demand for loans, interest rates will lower and so will savings. This circle will continue till equilibrium is found.
So we can see that savings do tend to rise as interest rates rise as apperent from the trendline.

YearReal_Interest_RateGross_National_Saving
2004-0.4563826943734931.38790
20051.9109227996206895.15750
2006-6.7740829804734325.03680
20074.1892732314180327.27400
2008-0.2368928722339763.21620
2009-5.0793034138157383.02620
20102.8797938234198686.90010
2011-4.3675045655038766.42100
20127.1253146013800169.68830
20134.6929749578236407.20550
20144.0204655158979868.63890
20155.8069063809372474.53710
20168.1644564079519714.32650
20174.0475561321833192.76420
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