None is necessarily true.
Even though you have your money in an interest-bearing savings vehicle, its value (purchasing power) may actually decrease if the interest rate is not at least as great as the inflation rate.
In periods of inflation, the value of money decreases over time. In periods of deflation, the value of money increases over time. It tends to be difficult to regulate an economy so the value of money remains constant over time.
The present value of money is greater than the future value in inflationary times. The opposite is true in deflationary times.
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In the US in the middle of the last century, inflation rates were consistently 2-3% per year and savings interest rates were perhaps 4-6%. Money saved actually increased in value, and the present value of money was greater than the future value. These days, inflation is perhaps a little lower, but savings interest rates are a lot lower, so savings does not outpace inflation the way it did. The truth or falsity of all these statements depends on where and when you're talking about.