An investment pays 6% compounded four times a year. How would you be able to find the annual growth factor and rate?
The annualized percentage rate is
(1.015)^4 -1 = 6.136%
What you are calling the annual growth facor is (1.015)^4 = 1.06136
To find the annual growth factor and rate of an investment that pays 6% compounded four times a year, we can use the following formulas:
Annual Growth Factor = (1 + (Interest Rate / Number of Times Compounded))^(Number of Times Compounded * Number of Years)
Annual Growth Rate = (Annual Growth Factor - 1) * 100
In this case, the interest rate is 6% (or 0.06 in decimal form), and it is compounded four times a year.
To find the annual growth factor:
1. Convert the interest rate to decimal form: 0.06.
2. Calculate the intermediate value: (1 + (0.06 / 4)).
3. Raise the intermediate value to the power of (4 * number of years).
Note: The number of years is not specified in the question, so you need that information to solve for the annual growth factor.
For example, if the investment is held for 5 years, the formula becomes:
Annual Growth Factor = (1 + (0.06 / 4))^(4 * 5) = (1.015)^20.
To find the annual growth rate:
1. Calculate the annual growth factor using the steps above.
2. Subtract 1 from the annual growth factor.
3. Multiply the result by 100 to convert it to a percentage.
For example, if the annual growth factor is 1.015 (calculated in the previous step):
Annual Growth Rate = (1.015 - 1) * 100 = 1.5%.
So, the annual growth factor is 1.015, and the annual growth rate is 1.5% for this particular investment that pays 6% compounded four times a year.