How long must one wait (to the nearest year) for an initial investment of $1,000 to triple in value if the investment earns 8 percent compounded annually? A)9 B)14 C)22 D)25 $3,000 = 1,000(1.08)ⁿ 3 = (1.08)ⁿ 14)27, or approx.14 yrs.= N

Question

Quizplus · Accepted Answer

We can use the formula A=P(1+r/n)^(nt) to solve for the number of years needed for the investment to triple, where A is the ending amount, P is the initial investment, r is the annual interest rate, n is the number of times compounded per year, and t is the number of years.

Plugging in the values given, we get:
$3,000 = $1,000(1+0.08/1)^(1t)
3 = (1.08)^t
Taking the logarithm of both sides, we get:
log(3) = t*log(1.08)
t = log(3)/log(1.08)
t ≈ 14

Therefore, it will take approximately 14 years for the investment to triple in value, so the best choice is B.

How Long Must One Wait (To the Nearest Year) for an Initial