At an annual interest rate of 10 percent,about how many years will it take $100 to triple in value?
A)8
B)10
C)12
D)14

Question

Quizplus · Accepted Answer

To triple in value, $100 would need to become $300. Using the formula for compound interest, we can determine how long it would take for an initial investment of $100 to grow to $300 at an annual interest rate of 10 percent:

$300 = $100(1 + 0.10)^t

Dividing both sides by $100:

3 = 1.10^t

Taking the logarithm of both sides:

log 3 = log 1.10^t

Using the rule of logarithms that says log a^b = b log a:

log 3 = t log 1.10

Dividing both sides by log 1.10:

t ≈ 11.47

Rounding to the nearest year, it would take about 12 years for $100 to triple in value at an annual interest rate of 10 percent. Therefore, the best choice is C.

At an Annual Interest Rate of 10 Percent,about How Many