(Advanced analysis) Kara has $2,000 to invest today that she wants to grow to $3,000 in ﬁve years. What annually compounded rate of interest would she have to earn to reach her goal?

Question

Quizplus · Accepted Answer

Using the formula for compound interest, we can solve for the annual interest rate needed:

$3,000 = $2,000(1+r)^5

Dividing both sides by $2,000, we get:

1.5 = (1+r)^5

Taking the fifth root of both sides, we get:

1.5^(1/5) = 1+r

Simplifying, we get:

r = 0.084 = 8.4%

Therefore, Kara would need to earn an annual interest rate of 8.4% to reach her goal.

(Advanced Analysis) Kara Has $2,000 to Invest Today That She