How long will it take money to double if it is invested at​ (A) 13​% compounded​ continuously? (B) 15​% compounded​ continuously? (2024)

FAQs

How long will it take money to double if it is invested at 15% compounded continuously? ›

At 15% compounded continuously, the investment doubles in about 4.62 years. (Round to two decimal places as needed.)

To convert this to months, we multiply it by 12: months = 0.47 * 12 = 5.64 months. Therefore, it will take approximately 5 years and 7 months for the investment to double at a 13% interest rate compounded monthly.

Years To Double: 72 / Expected Rate of Return

To calculate the time period an investment will double, divide the integer 72 by the expected rate of return. The formula relies on a single average rate over the life of the investment.

Answer and Explanation:

Let the amount invested be P=x so that amount accumulated after t years will be A=2x. We have r=0.14. The value of t can be found as follows. Thus, it will take approximately 5.037 years for the investment to double in value.

For simple interest, you want to double the amount of money. So take 100 divide by 15 the answer is about 6.7. It will take about 6.7 years.

The effective rate of 13% compounded monthly is 13.80%.

r is the nominal interest rate. n is the number of times interest is compounded in a year.

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.

Simply divide 72 by the interest rate to determine the outcome. At a 2% interest rate, it would take 36 years to double your money. At a 12% interest rate, it would only take six years to double your money. You can also use the Rule of 72 to approximate how much an amount would grow over a time period.

What is the 8-4-3 rule of compounding? In the 8-4-3 strategy, the average return of a particular investment amount for 8 years is 12 per cent/annum, while after that time period, it will take only half of that horizon, i.e., 4 years (total 12 years), to get a return of 12 per cent.

All you do is divide 72 by the fixed rate of return to get the number of years it will take for your initial investment to double. For example, if your investment earns 6% per year on average, you would take 72 divided by 6 to determine that it will take 12 years for your money to double.

How to double 1000 dollars? ›

How Can I Double $1000? If your employer offers a dollar-for-dollar match contribution, you can double $1,000 by investing it in your 401(k). Other than that, there's no easy or risk-free way to double $1,000—you can invest the money in individual stocks, but there will be risks involved.

The average annualized total return for the S&P 500 index over the past 90 years is 9.8%. Adjusted for inflation, it still comes to an annual return of around 7% to 8%. If you earn 7%, your money will double in a little over 10 years.

How the Rule of 72 Works. For example, the Rule of 72 states that $1 invested at an annual fixed interest rate of 10% would take 7.2 years ((72 ÷ 10) = 7.2) to grow to $2. In reality, a 10% investment will take 7.3 years to double (1.10^7.3 = 2).

For example, to double your money in six years, you would need a rate of return of 12%. MathWorks.

A 10% interest rate will double your investment in about 7 years (72 ∕ 10 = 7.2); an amount invested at a 12% interest rate will double in about 6 years (72 ∕ 12 = 6). Using the Rule of 72, you can easily determine how long it will take to double your money.

Thus, it will take 14.21 years for the money to double.

Does Compounded Continuously Mean Daily? Compounded continuously means that interest compounds every moment, at even the smallest quantifiable period of time. Therefore, compounded continuously occurs more frequently than daily.