Mr. Jones is contemplating retirement. He has just celebrated his 55th birthday and his net worth is $2 million. He hopes that after retirement he can maintain a lifestyle that costs him $100,000 per year in today's dollars (i.e., real dollars, inflation adjusted). For simplicity, assume that the cost occurs at the end of each year.

If he retires, he will invest all his net worth in government bonds that yield a safe nominal annual return of 5%. Inflation is expected to be 2% per year. Ignore taxes.

Mr. Jones thinks he will live until about 100. To insure against inflation risk, he's thinking about investing in an inflation-protected instrument such as TIPS. What minimal annual rate does the inflation-protected instrument have to offer so that Mr. Jones could sustain such a life style?