Some economists argue that people increase their savings when interest rates rise since they can earn more money. Suppose you were putting money away with the goal of raising $50,000 in five years. Would an increase in interest rates increase the amount of money you saved?

No. With a higher interest rate you could save less and still reach your goal of $50,000 in five years. More of the $50,000 could now come from your interest, hence less would have to come from your savings. In this case, where the future value is given, an increase in interest rates always lowers the principal required to reach that goal. The economists are discussing another scenario in which the future value is not specified. The evidence is that they are correct in that case, since higher interest rates make the future worth of one’s savings grow to a greater amount.