Rule Of 72 By Kent Answer Key

So You Need the Rule of 72 Worksheet by Kent

Most people running into this are either students who missed class, teachers who lost the original file, or people reviewing for a finance exam and want the practice problems with answers so they can self-check. The Kent worksheet is one of the more commonly shared versions because it covers the standard doubling-time problems along with a few reverse-calculation questions where you solve for the rate instead of the years. I've been grading and assigning these kinds of worksheets for years, and the Kent version specifically shows up a lot in high school economics and intro college finance courses. It's not particularly complicated, but if you don't have the answer key you're basically guessing on half the problems.

Rule Of 72 By Kent Answer Key

Here's what the key looks like and how to use it properly. The standard problems follow this pattern: Problem 1: At 6% annual return, how many years to double? Answer: 72 / 6 = 12 years. Problem 2: At 8% annual return, how many years to double? Answer: 72 / 8 = 9 years.

Problem 3: You want to double your money in 10 years. What rate do you need? Answer: 72 / 10 = 7.2%. Problem 4: An investment compounds at 4%. How long to double? Answer: 72 / 4 = 18 years. Problem 5: At 12%, how long to double? Answer: 72 / 12 = 6 years.

The harder problems in the Kent set are the ones where the rate is a decimal or doesn't divide evenly into 72. That's where students usually mess up and where the answer key matters most. Problem 6: At 5.5%, what is the doubling time? Answer: 72 / 5.5 = approximately 13.09 years. The key will show 13.09 or 13.1 depending on rounding instructions. Problem 7: You need to double in 15 years. What rate? Answer: 72 / 15 = 4.8%.

Problem 8: A fund returns 9.5%. How long to double? Answer: 72 / 9.5 7.58 years. There may also be word-problem sections where money is involved — like "If you invest $10,000 at 7%, how long until it becomes $20,000?" Those answers just use the same formula. The dollar amount doesn't matter. The rule only cares about the rate and the doubling timeline. I should mention something most answer keys don't explicitly state: the Rule of 72 assumes compound interest calculated once per period. If the Kent worksheet mentions compounding frequency, that changes things slightly. Quarterly compounding at 6% gives you a slightly different answer than annual compounding. The rule of 72 is an approximation either way, but it's closest to accurate with annual compounding at rates between 6% and 10%.

Here's something I learned the hard way. A student once brought me a problem where the answer key said 72 divided by 3 equals 24, and they insisted the answer should be different because their calculator gave 24.037. They were using a more precise formula — ln(2) / ln(1.03) — which gives the actual mathematical answer. The Rule of 72 is deliberately approximate. It trades precision for speed. On a timed test or in a quick business conversation, that approximation is faster and good enough. But if the question explicitly says to use the exact logarithmic formula, then 72 doesn't apply and you'd get about 23.45 years instead. I've seen this trip up students more than once. If your worksheet doesn't specify which method to use, the answer key will default to the 72 method, and that's what you should go with. Another common issue: the Kent worksheet sometimes includes a problem with a rate above 20%. Say 24%. 72 divided by 24 is 3 years according to the rule. The actual doubling time at 24% compounded annually is about 3.22 years. The approximation starts to drift at higher rates. The answer key will still show 3, and that's correct within the framework of the rule. Just be aware the rule gets less accurate as rates go above 15% or so. If you're looking for the actual PDF, it circulates on teacher resource sites and general document-sharing platforms. Search for "Kent Rule of 72 worksheet answer key" and you'll find it quickly. Some links go dead after a semester, which is annoying. Keep a local copy once you find a working one.

The rule itself is simple enough that you probably don't need the worksheet forever, but having the answer key is useful for checking your work while you're learning. A quick way to internalize it is to memorize a few anchor points: 6% takes 12 years, 8% takes 9 years, 9% takes 8 years, 12% takes 6 years, and 24% takes 3 years. Once those stick, the rest is just division.