Question

Joan invested 1,420 at the start of the year and found she had1,621.40 at the end of the year. What is the annual effective yield of her investment? Input your answer as a percentage to two decimal places but omit the

Answer 1

To find the annual effective yield of Joan's investment, you divide the end value of the investment ($1,621.40) by the start value ($1,420), raise this to the power of (1/number of years), and subtract 1. Doing this calculation shows Joan's investment had an annual effective yield of 14.18%.

Step-by-step explanation:

The annual effective yield of an investment is the percentage of interest that is earned on an investment over a year, taking into account the effects of compounding. To calculate the annual effective yield, we use the formula:

Annual Effective Yield = [(Ending Value / Beginning Value) ^ (1 / Number of Years)] - 1

In the student's case, Joan's investment at the start of the year was $1,420, and at the end of the year, her investment was worth $1,621.40.

To find the annual effective yield, we take the ending value and divide it by the beginning value:

(End Value / Start Value) = ($1,621.40 / $1,420)

This gives us a quotient of approximately 1.141831, which we can use in our formula for calculating the yield:

Annual Effective Yield = [1.141831^(1/1)] - 1

So, Annual Effective Yield = 1.141831 - 1 = 0.141831, or 14.18% when expressed as a percentage to two decimal places. Therefore, Joan's investment yielded an annual effective yield of 14.18%.