Double Your Money: The Rule of 72The Rule of 72 is a quick and simple technique for estimating one of two things: Show
The rule states that an investment or a cost will double when: [Investment Rate per year as a percent] x [Number of Years] = 72. When interest is compounded annually, a single amount will double in each of the following situations:  The Rule of 72 indicates than an investment earning 9% per year compounded annually will double in 8 years. The rule also means if you want your money to double in 4 years, you need to find an investment that earns 18% per year compounded annually. You can confirm the rationality of the Rule of 72 as follows: Find factors on the FV of 1 Table that are close to 2.000. (The factor of 2.000 tells you that the present value of 1.000 had doubled to the future value of 2.000.) When you find a factor close to 2.000, look at the interest rate at the top of the column and look at the number of periods (n) in the far left column of the row containing the factor. Multiply that interest rate times the number of periods and you will get the product 72. To use the Rule of 72 in order to determine the approximate length of time it will take for your money to double, simply divide 72 by the annual interest rate. For example, if the interest rate earned is 6%, it will take 12 years (72 divided by 6) for your money to double. If you want your money to double every 8 years, you will need to earn an interest rate of 9% (72 divided by 8). Here's another way to demonstrate that the Rule of 72 works. Assume you make a single deposit of $1,000 to an account and wish for it to grow to a future value of $2,000 in nine years. What annual interest rate compounded annually will the account have to pay? The Rule of 72 indicates that the rate must be 8% (72 divided by 9 years). Let's verify the rate with the format we used with the FV Table: To finish solving the equation, we search only the "n = 9" row of the FV of 1 Table for the FV factor that is closest to 2.000. The factor closest to 2.000 in the row where n = 9 is 1.999 and it is in the column where i = 8%. An investment at 8% per year compounded annually for 9 years will cause the investment to double (8 x 9 = 72). A. 9 years B. 8 years C. 27 years D. 12 years Solution(By Examveda Team)$$\eqalign{ & {\text{Let}}, \cr & {\text{Principal}} = Rs.\,100 \cr & {\text{Amount}} = Rs.\,200 \cr & {\text{Rate}} = r\% \cr & {\text{Time}} = 4\,{\text{years}} \cr & {\text{Now}}, \cr & A = P \times {\left[ {1 + \left( {\frac{r}{{100}}} \right)} \right]^n} \cr & 200 = 100 \times {\left[ {1 + \left( {\frac{r}{{100}}} \right)} \right]^4} \cr & 2 = {\left[ {1 + \left( {\frac{r}{{100}}} \right)} \right]^4} - - - - - - \left( i \right) \cr & {\text{If}}\,{\text{sum}}\,{\text{become}}\,{\text{8}}\,{\text{times}}\,{\text{in}}\,{\text{the}}\,{\text{time}}\,n\,{\text{years}} \cr & {\text{then,}} \cr & 8 = {\left( {1 + \left( {\frac{r}{{100}}} \right)} \right)^n} \cr & {2^3} = {\left( {1 + \left( {\frac{r}{{100}}} \right)} \right)^n} - - - - - - \left( {ii} \right) \cr & {\text{Using}}\,{\text{eqn}}\,\left( i \right)in\left( {ii} \right),\,{\text{we}}\,{\text{get}} \cr & {\left( {{{\left[ {1 + \left( {\frac{r}{{100}}} \right)} \right]}^4}} \right)^3} = {\left( {1 + \left( {\frac{r}{{100}}} \right)} \right)^n} \cr & {\left[ {1 + \left( {\frac{r}{{100}}} \right)} \right]^{12}} = {\left( {1 + \left( {\frac{r}{{100}}} \right)} \right)^n} \cr & {\text{Thus}},\,n = 12\,{\text{years}}. \cr} $$ 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. Nội dung chính 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.
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:
If 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: 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.) A sum of money placed at Compound Interest (C.I.) doubles itself in 5 years. It will amount to eight times itself at the same rate of interest in:-A. 7 yearsB. 10 yearsC. 15 yearsD. 20 yearsAnswer Verified Hint: To find the number of years in which Compound Interest amounts to eight times given that a sum of money placed at Compound Interest (C.I.) doubles itself in 5 years. We shall take the sum of the money, i.e. the principal amount be ‘X’. Now, according to the question, after 5 years, X becomes 2X, and after next five years, i.e. after 10 years, 2X will become 4X because of the same, and so on. We will use \[A\ \ =\ \ P\ {{\left( 1\ \ +\ \ \dfrac{R}{100} \right)}^{n}}\] . Let us take \[A\] as $2X$ , $P$ as $X$ and $n$ as $5$ . We shall put these values in the equation to find the answer. To find the number of years in which the sum that is given to us will become 8 times of itself, take \[A\] as $8X$ , $P$ as $X$ . After substitution and comparing both the equations, we will get the number of years. Complete step by step answer: So, the correct answer is “Option C”. Note: Be careful with the equation of CI \[A\ \ =\ \ P\ {{\left( 1\ \ +\ \ \dfrac{R}{100}
\right)}^{n}}\] . There can be a chance of making an error in this equation. We can also use the following method to find the answer to this question. How much a sum becomes double in 16 years?Let principal = P. Then S.I. = P and T = 16 yrs. Rate = 100 x P/P*16% = 6 ¼ % p.a. At what rate will a sum of money doubles itself in 10 years?Rate = 100/10 = 10%. How many years will a sum of money double itself?Given: the sum of money doubles itself. ∴ Time taken is 10 years. At what rate of compound interest a sum of money will double itself in 12 years?Let the principal be x. Then, the amount after 12 years be 2x. Let the rate of interest be R. ∴ The rate of interest is 25/3%. At what rate of compounded interest would an amount double itself in 4 years?R =18.20% compounded annually - at which rate money will double in 4 years. A certain sum of money doubles itself in 4 years at some rate of interest. In how many years will it become 32 times to itself?
At what rate of compound interest does a sum of money becomes 4 times of itself in 4 years?∴ Rate %=41.42% half yearly and 82.84% p.a.
How long will it take for an amount to become double of itself at 4% per annum simple interest?=(x×4100×x)years = 25 years.
At what rate of compound interest would an amount double itself in 3 years?∴R=25.99% per annum.
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Approximately at what rate of compound interest would an amount double itself in 4 years
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