Question

Bob has been investing $4,000 in stock at the end of every year for the past 8 years. If the account is currently worth $45,000, what was his annual return on this investment?a. 10.61%b. 10.91%c. 8.81%d. 9.55%e. 9.07%

Answer 1

d. 9.55%

Step-by-step explanation:

we can use the future value of an annuity formula to calculate Bob's annual return:

future value = annual contribution x FV annuity factor

future value = $45,000

annual contribution = $4,000

FV annuity factor = ?

FV annuity factor = future value / annual contribution = $45,000 / $4,000 = 11.25

FV annuity factor = [(1 + i)ⁿ - 1] / i

11.25 = [(1 + i)⁸ - 1] / i

11.25i = (1 + i)⁸ - 1

solving this problem is really complicated, but there is a much simple way to do it:

e) 11.25 x 0.0907 = (1 + 0.0907)⁸ - 1

1.020375 ≠ 1.0028

d) 11.25 x 0.0955 = (1 + 0.0955)⁸ - 1

1.0744 = 1.0744 ⇒ this option is correct