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Savings is not always beneficial for economical growth. National Income is defined as sum total of consumption and savings i.e. Y = C + S.
Now suppose there is increase in income, the additional income could be either saved or spent. If it is saved then marginal propensity to save will increase which means no economic activity has been undertaken with additional money. Hence, MPS is inversely proportional to economic spending.
So if additional income is always saved then it may act as hindrance for economical growth.
Savings aree beneficial for a country because it is a common sense where most of the people put their savings, it is always in the bank and the bank uses the deposits as a capital to make some investments where they can make a lot of money and because of that strategy, the bank helps the country to sustain the flow of currency so their economy will have a continuous growth.
Oops, yes! My bad. I ignored an important assumption in my post. In case of two-sector economy, S = I where I is investment. So yes, when people save money, they either keep it to themselves or keep it in banks. In case they keep money with themselves then it doesn't contribute to economic development but if they deposit it with bank, bank further lend it to others. Here, another concept comes into picture, the concept of Investment Multiplier. When banks lend money, the borrower further give money to someone else, the other person may deposit money into his bank. This way money is back into bank and bank can once again lend the same money to someone else. So, savings do contribute to economic development if it is channelled through banks.