Finance question

Question

Chang needs $4500 for a future project. He can invest $3000 now at an annual rate of 9%, compounded monthly. Assuming that no withdrawals are made, how long will it take for him to have enough money for his project? Do not round any intermediate computations, and round your answer to the nearest hundredth.

Answer 1

To find out how long it will take for Chang to have enough money for his project, we can use the following formula:

time = (log(final value / initial value)) / (log(1 + rate / frequency))

In this case, the initial value is 3000, the final value is 4500, the rate is 9%, and the frequency is monthly, so we can plug these values into the formula like this:

time = (log(4500 / 3000)) / (log(1 + 0.09 / 12))

Solving this equation, we find that it will take approximately 3.46 years for Chang to have enough money for his project.