Q. How to evaluate total savings?

Total savings

Remember that total savings is stated as S = S_H + S_G + S_R, sum of net savings from the household, government and rest of the world. As with S_H, S may be the observed amount of savings or total supply of savings. In the classical model, S_R and S_G are exogenous variables. S_G = NT - G and S_R = Im - X depend only on exogenous variables and are thus themselves exogenous. 

Only part of savings that is endogenous is household savings. Because household savings depend positively on real interest rate, total savings will depend positively on real interest rate. In the classical model we use S(r) to signify total savings and we have 

S(r) = S_H(r) + S_G + S_R.

Note that S_H, S_G, and/or S_R may very well be negative. For instance when S_G is negative, G > NT and government is a net borrower.