Solving for Time How long will it take $3,000 to reach $5,000 when it grows at 7 percent per year?
A)7.00 years
B)7.55 years
C)9.52 years
D)10.29 years

Question

Quizplus · Accepted Answer

We can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years. We want to solve for t.

Plugging in the given information, we get:

$5,000 = $3,000(1 + 0.07/1)^(1t)

Simplifying, we get:

1.6667 = (1.07)^t

Taking the logarithm of both sides, we get:

log(1.6667) = log(1.07)^t

Using the power rule of logarithms, we can bring the t down:

log(1.6667) = t * log(1.07)

Solving for t, we get:

t = log(1.6667)/log(1.07)

Using a calculator, we get:

t ≈ 7.55 years

Therefore, the best answer choice is B.

Solving for Time How Long Will It Take $3,000 to Reach