True or False?
The statement is false. It is true that an increase in the rate of interest increases the amount of future consumption that can be obtained by sacrificing a unit of current consumption. This by itself will induce people to shift their intertemporal consumption path from present goods to future goods. But if the initial level of saving is positive, a rise in the real interest rate increases the amount of future consumption that can be obtained from the existing savings level. As a result the level of wealth associated with the current level of measured income increases. This will cause people to increase current consumption and reduce savings, partially or completely offsetting the positive substitution effect.
An increase in the rate of interest thus has both a wealth and a substitution effect on saving. It increases the future consumption yielded by the existing level of savings, raising wealth, and causing people to increase both present and future consumption. This has the effect of reducing savings. At the same time, the rise in the interest rate makes future consumption more attractive relative to current consumption, causing savings to increase. It turns out that the substitution effect tends to dominate at lower levels of the real interest rate while the wealth effect tends to dominate at higher interest rate levels. For this reason, the savings function tends to have a positive slope at low interest rates and bend back on itself at high interest rates.