How long will it take $4,000 to grow to $7,500 if the investment earns interest at the rate of 14% / year compounded monthly? Round your answer to one decimal place.
A) 4.5 year(s)
B) 4.6 year(s)
C) 4.8 year(s)
D) 3.6 year(s)

Question

How long will it take $4,000 to grow to $7,500 if the investment earns interest at the rate of 14% / year compounded monthly? Round your answer to one decimal place. ​
A) 4.5 year(s)
B) 4.6 year(s)
C) 4.8 year(s)
D) 3.6 year(s)

Quizplus · Accepted Answer

The correct answer is A because the formula for compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times per year that the interest is compounded, and t is the number of years. In this case, we have P = $4,000, A = $7,500, r = 14%, n = 12 (since the interest is compounded monthly), and we want to find t. Plugging these values into the formula, we get $7,500 = $4,000(1 + 0.14/12)^(12t). Dividing both sides by $4,000 and simplifying, we get (1 + 0.14/12)^(12t) = 1.875. Taking the natural logarithm of both sides, we get 12t * ln(1 + 0.14/12) = ln(1.875). Dividing both sides by 12 * ln(1 + 0.14/12), we get t = 4.5 years (rounded to one decimal place).

How Long Will It Take $4,000 to Grow to $7,500