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). Free Important Civilization in Rajasthan 15 Questions 15 Marks 10 Mins Given: Rate (R) = 20% Formula used: S.I. = (P × R × T)/100 Where, S.I. → Simple Interest P → Principal R → Rate T → Time Calculations: Let the sum of money be Rs. P. So, A = 3P And S.I. = A - P = 3P – P = 2P Thus T = (100 × S.I.)/(P × R) ⇒ T = (100 × 2P)/(P × 20) = 10 years ∴ The required time is 10 years. Latest RSMSSB Forest Guard Updates Last updated on Oct 29, 2022 The RSMSSB Forest Guard Admit Card is out. For Forester Post, admit cards can be downloaded from 28th October 2022 and for Forest Guard, admit cards will be available from 4th November 2022. The exam for Forester will be conducted on 6th November 2022 and the exam for Forest Guard will be conducted on 12th & 13th November 2022. Total vacancies have been increased to 2399. The selection process consists of 5 stages i.e. Written Test, Physical Standard & Efficiency Test (PST & PET), Interview, Medical Examination, and finally Document & Character Verification. The candidates must also go through the RSMSSB Forest Guard Previous Years’ Paper. Ace your Interest preparations for Simple Interest with us and master Quantitative Aptitude for your exams. Learn today! Simple Interest: A = P(1+rt)P: the principal, the amount invested A: the new balance t: the time r:the rate, (in decimal form)Ex1: If $1000 is invested now with simple interest of 8% per year. Find the new amount after two years. P = $1000, t = 2 years, r = 0.08. A = 1000(1+0.08(2)) = 1000(1.16) = 1160Compound Interest:P:the principal, amount invested A: the new balance t: the time r:the rate, (in decimal form) n: the number of times it is compounded. Ex2:Suppose that $5000 is deposited in a saving account at the rate of 6% per year. Find the total amount on deposit at the end of 4 years if the interest is: P =$5000, r = 6% , t = 4 yearsa) simple : A = P(1+rt) A = 5000(1+(0.06)(4)) = 5000(1.24) = $6200b) compounded annually, n = 1: c) compounded semiannually, n =2: A = 5000(1 + 0.06/2)(2)(4) = 5000(1.03)(8) = $6333.85d) compounded quarterly, n = 4: A = 5000(1 + 0.06/4)(4)(4) = 5000(1.015)(16) = $6344.93e) compounded monthly, n =12: A = 5000(1 + 0.06/12)(12)(4) = 5000(1.005)(48) = $6352.44f) compounded daily, n =365: A = 5000(1 + 0.06/365)(365)(4) = 5000(1.00016)(1460) = $6356.12Continuous Compound Interest:Continuous compounding means compound every instant, consider investment of 1$ for 1 year at 100% interest rate. If the interest rate is compounded n times per year, the compounded amount as we saw before is given by: A = P(1+ r/n)ntthe following table shows the compound interest that results as the number of compounding periods increases: P = $1; r = 100% = 1; t = 1 year
As the table shows, as n increases in size, the limiting value of A is the special number e = 2.71828If the interest is compounded continuously for t years at a rate of r per year, then the compounded amount is given by: A = P. e rtEx3: Suppose that $5000 is deposited in a saving account at the rate of 6% per year. Find the total amount on deposit at the end of 4 years if the interest is compounded continuously. (compare the result with example 2) P =$5000, r = 6% , t = 4 years A = 5000.e(0.06)(4) = 5000.(1.27125) = $6356.24Ex4: If $8000 is invested for 6 years at a rate 8% compounded continuously, find the new amount: P = $8000, r = 0.08, t = 6 years. A = 8000.e(0.08)(6) = 8000.(1.6160740) = $12,928.60Equivalent Value:When a bank offers you an annual interest rate of 6% compounded continuously, they are really paying you more than 6%. Because of compounding, the 6% is in fact a yield of 6.18% for the year. To see this, consider investing $1 at 6% per year compounded continuously for 1 year. The total return is: A = Pert = 1.e(0.06)(1) = $1.0618 If we subtract from $1.618 the $1 we invested, the return is $0.618, which is 6.18% of the amount invested. The 6% annual interest rate of this example is called the nominal rateThe 6.18% is called the effective rate.
Ex6: An amount is invested at 7.5% per year compounded continuously, what is the effective annual rate? the effective rate = er - 1 = e 0.075 - 1 = 1.0079 - 1 = 0.0779 = 7.79%Ex7: A bank offers an effective rate of 5.41%, what is the nominal rate? er - 1 = 0.0541 er = 1.0541 r = ln 1.0541 then r = 0.0527 or 5.27%Present Value:If the interest rate is compounded n times per year at an annual rate r, the present value of a A dollars payable t years from now is:If the interest rate is compounded continuously at an annual rate r, the present value of a A dollars payable t years from now is P = A. e-rtEx8: how much should you invest now at annual rate of 8% so that your balance 20 years from now will be $10,000 if the interest is compounded a) quarterly: P = 10,000.(1+0.08/4)-(4)(20)= $ 2,051.10 b) continuously: P = 10,000.e-(0.08)(20) = $2.018.974.3: The Growth, Decline Model:Same formulas will be applied for population, cost ...:Growth: P(t) = Po . ektDecline: P(t) = Po . e-kt
For compounded continuously, the time T it takes to double the price, population or balance using k as the rate of change, the growth rate or the interest rate is given by: ===>Note: the time it takes to triple it is T = ln3/k and so on..., (only if it is compounded continuously).Ex9: The growth rate in a certain country is 15% per year. Assuming exponential growth : a) find the solution of the equation in term of Po and k. b) If the population is 100,000 now, find the new population in 5 years. c) When will the 100,000 double itself? Answer: a) Po. e 0.15t; b) 211,700; c) 4.62 yearsEx10: If an amount of money was doubled in 10 years, find the interest rate of the bank. Answer: 6.93%Ex11: In 1965 the price of a math book was $16. In 1980 it was $40. Assuming the exponential model : a) Find k (the average rate) and write the equation. b) Find the cost of the book in 1985. c) After when will the cost of the book be $32 ? Answer: a) 6.1%; b) $ 54.19; c) T = 11.36 yearsEx12: How long does it take money to triple in value at 6.36% compounded daily? Answer: 17.27 yearsEx13: A couple want an initial balance to grow to $ 211,700 in 5 years. The interest rate is compounded continuously at 15%. What should be the initial balance? Answer: $100,000Ex14: The population of a city was 250,000 in 1970 and 200,000 in 1980 (Decline). Assuming the population is decreasing according to exponential-decay, find the population in 1990. Answer: 160,000How long will it take money to triple if it earns 9 compounded quarterly?Answer and Explanation:
The answer to the question is 14.3 years.
How long will it take money to triple itself if invested at 8% compounded quarterly?Answer: Approximately 13 years.
How do you figure out how long it will take an investment to triple?Rule of 115: If 115 is divided by an interest rate, the result is the approximate number of years needed to triple an investment. For example, at a 1% rate of return, an investment will triple in approximately 115 years; at a 10% rate of return it will take only 11.5 years, etc.
How long does it take money to triple at 6% compounded quarterly?1 Answer. Joe D. It will approximately take 18 years 10 months.
|
How long in years will it take money to triple if it earns 9% compounded quarterly *?
zusammenhängende Posts
Urheberrechte © © 2024 ihoctot Inc.
