(Advanced analysis) Tani invests $100 in a ﬁnancial asset earning an annually compounded interest rate of 5 percent. In about how many years will her investment be worth $150?
A) 5.2
B) 6.8
C) 8.3
D) 10

Question

Quizplus · Accepted Answer

Using the formula for compound interest, we have:

$150 = $100(1 + 0.05)^n

Solving for n:

1.5 = 1.05^n

Taking the natural logarithm of both sides:

ln(1.5) = n ln(1.05)

n = ln(1.5) / ln(1.05)

n ≈ 8.3

Therefore, Tani's investment will be worth $150 after about 8.3 years, so the best choice is C.

(Advanced Analysis) Tani Invests $100 in a ﬁNancial Asset Earning