To attract world-class post-docs, Kronos Labs wants to establish a research fund that will provide $25,000/year for 15 years beginning at some future date. Kronos has $34,250 now it can put immediately away at a 9% interest and can pay $7,000 per year into the fund starting next year for a to be determined number of years, say X. What minimum number of years, X, does Kronos need to make payments before it can begin to offer the research fund to post-docs? I suggest you consider the cash flow diagram below: