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In how many years will a sum of money double itself with the rate of 10% per annum simple interest?Answer Verified
Hint: To solve the problem, we should know the definition of annual simple interest. We have, Complete step-by-step answer: Note: While solving questions related to principal interest, it is important to keep in mind that simple interest calculated from the formula, Simple Interest (I) = $\dfrac{P\times R\times t}{100}$ , doesn’t represent the total amount of money. In fact, the total amount is the sum of Principal amount (P) and simple interest. Thus, in this case, when money was doubled, the total amount was 2P and simple interest was P.
Cal P. How long will it take for money to triple if it is invested at the following rates? 1) 3% compounded monthly 2) 2% compounded annually More 1 Expert Answer
Andrew M. answered • 01/20/18 Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors A = p(1+r/n)nt A = future amount p = principal investment r = interest rate in decimal form n = # times compounded per year t = time in years 3p = p(1+0.03/12)12t 3 = 1.002512t Take log of both sides log 3 = log 1.002512t log 3 = 12t(log 1.0025) t = (log 3)/(12 log 1.0025) t = 36 2/3 years = 36 years 8 months Problem 2: 3p = p(1 + 0.02/1)1t 3p = p(1.02)t Work the same way as problem 1 Still looking for help? Get the right answer, fast.ORFind an Online Tutor Now Choose an expert and meet online. No packages or subscriptions, pay only for the time you need. In this section we cover compound interest and continuously compounded interest. Use the compound interest formula to solve the following. Example: If a $500 certificate of deposit earns 4 1/4% compounded monthly then how much will be accumulated at the end of a 3 year period?
Answer: At the end of 3 years the amount is $576.86.
Example: A certain investment earns 8 3/4% compounded quarterly. If $10,000 is invested for 5 years, how much will be in the account at the end of that time period? Answer: At the end of 5 years the account have $15,415.42 in it. The basic idea is to first determine the given information then substitute the appropriate values into the formula and evaluate. To avoid round-off error, use the calculator and round-off only once as the last step.
One important application is to determine the doubling time. How long does it take for the principal in an account earning compound interest to double? Example: How long does it take to double $1000 at an annual interest rate of 6.35% compounded monthly?
Answer: The account will double in approximately 10.9 years. The key step in this process is to apply the common logarithm to both sides so that we can apply the power rule and solve for time t. Use the calculator in the last step and round-off only once. Example: How long will it take $30,000 to accumulate to $110,000 in a trust that earns a 10% return compounded semiannually?
Answer: Approximately 13.3 years. Example: How long will it take our money to triple in a bank account with an annual interest rate of 8.45% compounded annually?
Answer: Approximately 13.5 years to triple. Make a note that doubling or tripling time is independent of the principal. In the previous problem, notice that the principal was not given and that the variable P cancelled. Use the continuously compounding interest formula to solve the following. Example: If a $500 certificate of deposit earns 4 1/4% annual interest compounded continuously then how much will be accumulated at the end of a 3 year period?
Answer: the amount at the end of 3 years will be $576.99. Example: A certain investment earns 8 3/4% compounded continuously. If $10,000 dollars is invested, how much will be in the account after 5 years?
Answer: The amount at the end of five years will be $15,488.30. The previous two examples are the same examples that we started this chapter with. This allows us to compare the accumulated amounts to that of regular compound interest.
As we can see, continuous compounding is better, but not by much. Instead of buying a new car for say $20,000, let us invest in the future of our family. If we invest the $20,000 at 6% annual interest compounded continuously for say, two generations or 100 years, then how much will our family have accumulated in that time? The answer is over 8 million dollars. One can only wonder actually how much that would be worth in a century.
Given continuously compounding interest, we are often asked to find the doubling time. Instead of taking the common log of both sides it will be easier take the natural log of both sides, otherwise the steps are the same. Example: How long does it take to double $1000 at an annual interest rate of 6.35% compounded continuously?
Answer: The account will double in about 10.9 years. The key step in this process is to apply the natural logarithm to both sides so that we can apply the power rule and solve for t. Use the calculator in the last step and round-off only once. Example: How long will it take $30,000 to accumulate to $110,000 in a trust that earns a 10% annual return compounded continuously?
Answer: Approximately 13 years. Example: How long will it take our money to triple in a bank account with an annual interest rate of 8.45% compounded continuously?
Answer: Approximately 13 years. YouTube Video: --- How long will an amount of triple at 12% per annum?The answer will be the number of years needed for that initial deposit to double-in this case 6 years. Originally Answered: How long will it take a certain some of money to triple itself at 12% per annum compound interest? Nine years and 248.8998 days.
How long will it take a sum to triple itself at the rate of 10% compounded semi annually?The answer to the question is 14.3 years.
How long will it take to triple an investment?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 will it take money to triple if it is invested at compounded?How long will it take for an investment to triple if it is compounded continuously at 12%? Or, t =1.0986/0.12 = 9.155 i.e., 9.16 years Ans.
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