How long does it take to double an investment if it is invested at a rate of 8% compounded continuously?
Double Your Money: The Rule of 72
The Rule of 72 is a quick and simple technique for estimating one of two things:
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).
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Your savings account balances and investments can grow more quickly over time through the magic of compounding. Use the compound interest calculator above to see how big a difference it could make for you.
Using this compound interest calculator
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Here’s a deeper look at how compounding works:
What is compound interest?
For savers, the definition of compound interest is basic: It’s the interest you earn on both your original money and on the interest you keep accumulating. Compound interest allows your savings to grow faster over time.
In an account that pays compound interest, such as a standard savings account, the return gets added to the original principal at the end of every compounding period, typically daily or monthly. Each time interest is calculated and added to the account, the larger balance earns more interest, resulting in higher yields.
For example, if you put $10,000 into a savings account with a 0.50% annual yield, compounded daily, you’d earn $51 in interest the first and second years, and $53 the third year. After 10 years of compounding, you would have earned a total of $513 in interest.
But remember, that’s just an example. For longer-term savings, there are better places than savings accounts to store your money, including Roth or traditional IRAs and CDs.
Compounding investment returns
When you invest in the stock market, you don’t earn a set interest rate but rather a return based on the change in the value of your investment. When the value of your investment goes up, you earn a return.
If you leave your money and the returns you earn invested in the market, those returns are compounded over time in the same way that interest is compounded.
If you invested $10,000 in a mutual fund and the fund earned a 7% return for the year, you’d gain about $700, and your investment would be worth $10,700. If you got an average 7% return the following year, your investment would then be worth about $11,500.
Over the years, your investment can really grow: If you kept that money in a retirement account over 30 years and earned that average 7% return, for example, your $10,000 would grow to more than $76,000.
In reality, investment returns will vary year to year and even day to day. In the short term, riskier investments such as stocks or stock mutual funds may actually lose value. But over a long time horizon, history shows that a diversified growth portfolio can return an average of 6% to 7% annually. Investment returns are typically shown at an annual rate of return.
The average stock market return is historically 10% annually, though that rate is reduced by inflation. Investors can currently expect inflation to reduce purchasing power by 2% to 3% a year.
Compounding can help fulfill your long-term savings and investment goals, especially if you have time to let it work its magic over years or decades. You can earn far more than what you started with.
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Compounding with additional contributions
As impressive as compound interest might be, progress on savings goals also depends on making steady contributions.
Let’s go back to the savings account example above. We started with $10,000 and ended up with a little more than $500 in interest after 10 years in an account with a 0.50% annual yield. But by depositing an additional $100 each month into your savings account, you’d end up with $21,821 after 10 years, when compounded daily. The interest would be $821 on total deposits of $22,000.
How do you calculate time to double your investment?
The Rule of 72 is a calculation that estimates the number of years it takes to double your money at a specified rate of return. If, for example, your account earns 4 percent, divide 72 by 4 to get the number of years it will take for your money to double. In this case, 18 years.
How long does it take to double your money at 8 percent?
The principle is simple. Divide 72 by the annual rate of return to figure how long it will take to double your money. For example, if you earn an 8 percent annual return, it will take about 9 years to double. So the higher the return, the faster you can double your money.
How do you calculate compounded continuously doubling time?
When interest is compounded a given number of times per year use the formula A(t)=P(1+rn)nt. When interest is to be compounded continuously use the formula A(t)=Pert. Doubling time is the period of time it takes a given amount to double.
How long does it take to double your investment if the interest rate is 12 %?
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. where Y and r are the years and interest rate, respectively.