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Fed Chair Janet Yellen and central bank policymakers are very political, and Yellen should be "ashamed" of what she's doing to the country, Trump said, adding the Fed is not even close to being independent.
Trump said rates are being kept lower to bolster Obama's legacy. "Any increase at all will be a very, very small increase because they want to keep the market up so Obama goes out and let the new guy ... raise interest rates ... and watch what happens in the stock market."
Doubting whether rates would change while Obama remains in office, Trump said: "[Obama] wants to go out. He wants to play golf for the rest of this life. And he doesn't care what's going to happen after January."
In response to Trump's charges about politics influencing the central bank, Minneapolis Fed President Neel Kashkari told CNBC in a separate interview on Monday there's no truth to that notion.
American savers are the worst hit by the Fed's easy monetary policies, Trump said. "The ones who did it right — they saved their money [and] they cut down on their mortgages, ... and now they're practically getting zero interest on the money."
Ariel Investments Vice Chairman Charles Bobrinskoy told CNBC the Fed deserves to be criticized for missing opportunities to raise interest rates and for hurting savers and pension plans. But he said it is "dangerous" and "not healthy" for Trump to question the Fed's integrity.
"I don't think Janet Yellen is making her decisions based on trying to help Obama or Clinton. I think they have a view that the world economy is weak enough that it's not a great time to raise rates. I don't happen to share that view, but I don't think this is political," he told CNBC's "Squawk on the Street" on Monday.
As a real estate businessman, Trump said: "I love low interest rates," but for the good of the nation, rates should be higher.
"If I refinance something, I can get money for almost nothing," Trump said. But knocking Obama for the national debt going to $19.5 trillion under his watch, Trump said the debt needs to be reduced because higher rates would make interest payments exorbitant.
"These crazy, low interest rates, they're not always going to be this way ... because of market [conditions]," he said.
— CNBC's Tom DiChristopher contributed to this story.