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).
Jump to
RD Sharma Solutions Class 8 Mathematics Solutions for Compound Interest Exercise 14.2 in Chapter 14 - Compound InterestQuestion 29 Compound Interest Exercise 14.2 Find the rate at which a sum of money will double itself in 3 years, if the interestis compounded annually. Answer: Given details are, Time = 3 years Let rate be = R % Also principal be = P So, amount becomes = 2P By using the formula, A = P (1 + R/100)^n 2P = P (1 + R/100)^3 (1 + R/100)^3 = 2 (1 + R/100) = 21/3 1 + R/100 = 1.2599 R/100 = 1.2599-1 = 0.2599 R = 0.2599 × 100 = 25.99 ∴ Required Rate is 25.99% per annum
Video transcript [Music] hello dear student i am sunita nair from leader learning and i am here to do the sum for you which is find the rate at which a sum of money will double itself in three years if the interest is compounded annually so i'll show you how to do the sum now let's put down the formula that we know for compound interest so compound interest is given by this formula the amount right the amount is equal to let me put on the formula first p into 1 plus r by 100 raised to the power of n right where a is equal to the amount which is the principle [Music] plus the compound interest all right principle plus the compound interest then we have p of course is the principle r is the rate of interest per annum and n is the time period in years so i shall put number of years so let's substitute the values we know find the rate at which the sum of money will double itself in this case if it's going to double itself that means a is going to be twice the principle all right so let's substitute that value so we have 2p is equal to p into 1 plus r by 100 raised to the power of 3 because the time period is 3 years right so if i take 2p over p i am transferring p from the right hand side to the left hand side this will be equal to 1 plus r by 100 raised to 3. so p and p cancel and i have 2 is equal to 1 plus r by 100 raised to 3. now i'll take the cube root on both sides so i'll get cube root of 2 is equal to cube root of the right hand side which is 1 plus r by 100 raised to 3. now the cube root of any number raised to the power of 3 is the number itself right is the term itself so i have cube root of 2 which is 1.2599 is equal to one plus r by hundred or one point two five nine nine minus one gives me r by hundred on the left hand side i will get 0.2599 is equal to r by 100 or r is equal to by cross multiplication 0.25 multiplied by 100 which is equal to 25.99 so the rate therefore is 25.99 percent per annum i hope you understood the solution do drop in a comment if there if you find any difficulty visit our channel there are more homework solutions and subscribe to it for updates as well thank you Was This helpful? On what sum of money will the simple interest for 3 years at 8 percent per annum be half of the compound interest on Rs 800 for 2 years at 10 percent per annum?Answer (C) 1750 Rs.
In what time will a sum of money be three times of itself the rate of interest being 20% per annum?=>N=10 years. Was this answer helpful?
In what time a sum of money becomes 3 times of itself at simple interest rate of 10% per annum?∴ Time is 8 years.
At what rate percent will a sum of money becomes 9 by 4 of itself in 2 years?The rate of interest is 50 % per annum.
Here, a sum of money becomes 9/4 of itself in 2 years.
|
At what rate a sum of money will becomes eight times of itself in 3 years if the interest compounded yearly?
zusammenhängende Posts
Urheberrechte © © 2024 de.ketajaman Inc.
