To calculate how long it will take for a $2,200 investment to increase to $10,000 at an interest rate of 6.5 percent, we need to use the formula for compound interest.The formula for compound interest is:A = P(1 + r/n)^(nt)Where:A is the final amountP is the principal amount (initial investment)r is the annual interest rate (expressed as a decimal)n is the number of times interest is compounded per yeart is the number of yearsIn this case, the principal amount (P) is $2,200, the final amount (A) is $10,000, and the annual interest rate (r) is 6.5 percent, which is equivalent to 0.065 as a decimal.Let's assume that interest is compounded annually, so n is equal to 1.Now, let's plug in the given values into the formula and solve for t:$10,000 = $2,200(1 + 0.065/1)^(1*t)Simplifying the equation, we get:4.5455 = (1.065)^tTo solve for t, we can take the logarithm of both sides of the equation:log(4.5455) = log((1.065)^t)Using logarithm properties, we can bring down the exponent:log(4.5455) = t*log(1.065)Now, we can isolate t by dividing both sides of the equation by log(1.065):t = log(4.5455)/log(1.065)Using a calculator, we can find that t is approximately 15.29 years.Therefore, it will take approximately 15.29 years for a $2,200 investment to increase to $10,000 at an interest rate of 6.5 percent compounded annually.
FAQs
How long will it take to increase a $2,200 investment to $10,000 if the interest rate is 6.5 percent? - brainly.com? ›
Final answer:
How long will it take an investment of $10000 to double if the investment earns interest at the rate of 8% compounded continuously? ›For example, if an investment scheme promises an 8% annual compounded rate of return, it will take approximately nine years (72 / 8 = 9) to double the invested money. Note that a compound annual return of 8% is plugged into this equation as 8, and not 0.08, giving a result of nine years (and not 900).
How long will it take for an investment to double in value if it earns 6% compounded continuously? ›Answer and Explanation:
The expression for the compound interest amount for continuously compounding. Substitute the known values. Thus it will take 11.55 year.
We know that the simple interest formula is I = PRT, where I is the interest, P is the principal amount, R is the rate, and T is the time in years. We can rearrange this formula to solve for T: T = I / (PR). Substituting the given values, we get T = P11,200 / (P40,000 * 0.12) = 2.33 years.
How long in years will it take for an investment of $2000 to double in value if the interest rate is 6.5% per year compounded continuously? ›Final answer:
For a 6.5% interest rate, the time it takes to double is approximately 10.67 years, and the closest answer provided is 10.65 years.
Final answer:
It will take approximately 15.27 years to increase the $2,200 investment to $10,000 at an annual interest rate of 6.5%.
This means that the investment will take about 12 years to double with a 6% fixed annual interest rate. This calculator flips the 72 rule and shows what interest rate you would need to double your investment in a set number of years.
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Final answer:
It will take approximately 11.5 years for the investment of $9,000 to double if it earns interest at a rate of 6% per year compounded continuously.
It will take a bit over 10 years to double your money at 7% APR. So 72 / 7 = 10.29 years to double the investment.
At what rate of simple interest will $5000 amount to $6050 in 3 years 4months? ›
Solution, The rate of interest for which simple interest $5000 amounts to $6050 in 3 years, 4 months is 6.3%. Hence, the rate of interest for which simple interest $5000 amounts to $6050 in 3 years, 4 months is 6.3 %.
How much is $1000 worth at the end of 2 years if the interest rate of 6% is compounded daily? ›Hence, if a two-year savings account containing $1,000 pays a 6% interest rate compounded daily, it will grow to $1,127.49 at the end of two years.
What is the compound interest on 500 for 2 years at 10 pa? ›Let the principal be 'P'. ∴ The compound Interest is Rs 525.
Will my investments double every 7 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 (1.107.3 = 2). The Rule of 72 is reasonably accurate for low rates of return.
How long will it take $2000 invested at 8% to double? ›The calculated value of the number of years required for the investment of $2,000 to become double in value is 9 years.
Will my money double in 5 years? ›Alternatively you can calculate what interest rate you need to double your investment within a certain time period. For example if you wanted to double an investment in 5 years, divide 72 by 5 to learn that you'll need to earn 14.4% interest annually on your investment for 5 years: 14.4 × 5 = 72.
How long will it take an investment of $9000 to double if the investment earns interest at the rate of 9% compounded continuously? ›Taking the natural logarithm of both sides, we have 0.09t = ln(2). Dividing both sides by 0.09, we find t ≈ ln(2)/0.09 ≈ 7.645. Therefore, it will take approximately 7.6 years for an investment of $9,000 to double if it earns interest at a rate of 9% per year compounded continuously.
How long would $100 000 take to double at a simple interest rate of 8? ›Expert-Verified Answer
It will take 12.5 years to double the amount of $100,000 with a rate of 8%.
Answer and Explanation:
Since it is compounded semi-annually, the interest rate would be 8% / 2 = 4%. For semi-annual, the number of years would be 17.7 / 2 = 8.8. Hence, it will take 8.8 years to double the investment.
It takes approximately 13.86 years for a $7,000 investment to double with a 5% annual interest rate when compounded continuously. Where N is the number of years, ln represents the natural logarithm, and r is the annual interest rate (expressed as a decimal). N = 13.86 years (rounded to two decimal places).