True or false: negative real interest rates imply that if you save today, you can purchase a smaller basket of goods and services in the future, relative to the basket you could have consumed today.
This statement is true. Negative real interest rates mean that your money will lose value and you will come to be able to buy less with it.
Real interest rates are interest rates that are adjusted for inflation. In other words, let us say that you get an interest rate of 10% on your savings. That sounds like a lot. But now imagine that the rate of inflation is 5%. That cuts in half your real return on your savings. Now imagine that the rate of inflation is 10%. At this point you are actually losing the value of your money. This is because inflation is taking away the value of the money more quickly than the interest is building that value.
What this means is that you would be able to buy less of this basket of goods and services after you save. The money that you put in the bank today will be worth more than the money that you withdraw from the bank in the future.
Thus, this statement is true because negative interest rates take away the value of saved money.