How many years will it take an investment to triple?
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Have you always wanted to be able to do compound interest problems in your head? Perhaps not... but it's a very useful skill to have because it gives you a lightning fast benchmark to determine how good (or not so good) a potential investment is likely to be. Show
The rule says that to find the number of years required to double your money at a given interest rate, you just divide the interest rate into 72. For example, if you want to know how long it will take to double your money at eight percent interest, divide 8 into 72 and get 9 years. Interest Rate:%Years Required for Principal to Double Exact Answer: Rule of 72 Estimate:(We're assuming the interest is annually compounded, by the way.) As you can see, the "rule" is remarkably accurate, as long as the interest rate is less than about twenty percent; at higher rates the error starts to become significant. You can also run it backwards: if you want to double your money in six years, just divide 6 into 72 to find that it will require an interest rate of about 12 percent. Years to doubleyour investmentRequired Interest Rate Exact Answer:% Rule of 72 Estimate:% Y = 72 / r and r = 72 / Y Compound Interest CurveSuppose you invest $100 at a compound interest rate of 10%. The rule of 72 tells you that your money will double every seven years, approximately: YearsBalanceNow$1007$200(doubles every14$400 seven years)21$800If you graph these points, you start to see the familiar compound interest curve: Practice using the Rule of 72It's good to practice with the rule of 72 to get an intuitive feeling for the way compound interest works. So... Why Stop at a Double?There's nothing sacred about doubling your money. You can also get a simple estimate for other growth factors, as this calculator shows: Find years needed for my money to ...Double Triple Grow by a factor of Estimate to UseDivide the interest rate into Why Does the Rule of 72 Work?If you want to know more, see this explanation of why the rule of 72 works. (Brace yourself, because it's slightly geeked out.) Michael J. answered • 03/05/15 Tutor 5 (5)Best Afterschool Tutor to Prepare You For Your Regents See tutors like this See tutors like this You will use the formula
A = P(1 + (r/n))nt
where: A = accumulated amount P = investment t = time r = interest rate n = number of times compounded per year
P = P A = 3P r = 0.05 n = 1 t = 1
Substituting these values into the formula,
3P = P(1 + 0.05)t
Divide by P on both sides of equation.
3 = 1.05t
Log both sides of equation
log(3) = log(1.05)t
Bring the exponent t down as the coefficient of the log(1.05)
log(3) = t log(1.05)
Divide by log(1.05) on both sides of equation
t = log(3) / log(1.05) t = 22.52
It will take 22.52 years to triple the investment at interest rate of 5%.
Upvote • 0 Downvote More Report To the nearest year, it will it take#18#years for an investment to triple, if it is continuously compounded at#6%#per year. Explanation:An investment#P#compounded continuously at a rate of interest of#r%#per year for#t#years becomes #Pe^(rt)#, where#e#is the Euler's number, an irrational number, after Leonhard Euler whose value is#2.71828182845904523536....#and logarithm to base#e#is mentioned as#ln#, known as natural log. As in#t#years, investment triples, it becomes#3P# Hence#Pe^(0.06t)=3P# or#e^(0.06t)=3# i.e.#0.06t=ln3=1.0986122887# therefore#t=1.0986122887/0.06=18.31# hence to the nearest year, it will it take#18#years for an investment to triple, if it is continuously compounded at#6%#per year. How many years will it take for your money to triple?For typical interest rates, the time it takes to double is about 72 divided by the interest rate. , so it takes about ten years to double. If you multiply by 1.5, you get a rough idea of how long it takes to triple, so 15 years (the actual answer is 15.19 years, or 15 years, 70 days).
How many years will it take an investment to triple if the interest rate is 8% compounded annually?Answer and Explanation:
The answer to the question is 14.3 years. There are two ways to get this answer. 1. Rule 115 where you divide 115 by the interest rate (115/8 = 14.3).
How many years will it take for an investment to triple if the interest rate is 12% compounded annually?Answer and Explanation: Hence, it will take 9.2 years for an investment to triple if it is compounded continuously at 12%.
How many years would it take for your investment to triple if it were invested at 5% compounded annually?Answer and Explanation: The calculated value of the time required to triple the money is 22.517 years.
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