Final Answer:
It will take approximately 7.69 years for an investment of $5,400.00 to grow to $26,900.00 if it is invested at an annual rate of 9.2%, compounded 6 times per year.
Step-by-step explanation:
Investing money is a process of committing funds to an endeavor with the expectation of achieving a profit or material gain. The most common type of investment is the purchase of stocks, bonds, mutual funds, real estate, or other financial instruments. When investing, one must consider the expected return on the investment, as well as the associated risks. The expected return on an investment can be calculated using the time value of money concept, which takes into account the rate of return, the length of time the money is invested, and the compounding frequency.
In this case, the rate of return is 9.2%, the length of time is 7.69 years, and the compounding frequency is 6 times per year. To calculate the expected return on the investment, we must first calculate the future value of the investment. The future value of an investment is calculated by multiplying the present value (in this case, $5,400.00) by the compounding frequency raised to the power of the length of time (in this case, 6 times 7.69 years). This results in a future value of $26,900.00.
To calculate the length of time it will take for the investment to grow to $26,900.00 at a rate of 9.2%, we must use the formula for compound interest, which states that the future value of an investment is equal to the present value multiplied by (1 + the rate of return) raised to the power of the length of time. Solving for the length of time gives us a result of 7.69 years.
Therefore, it will take approximately 7.69 years for an investment of $5,400.00 to grow to $26,900.00 if it is invested at an annual rate of 9.2%, compounded 6 times per year.