Question

Select the correct answer from each drop-down menu. Roger invested a certain amount into an account with an interest rate of 10 percent compounded annually. It will take approximately years before Roger’s investment is triple the original amount invested. If his friend invested twice as much as Roger in the same bank, it takes time for his investment to triple the original amount invested

Answer 1

To solve this compound interest problem, we need to find the time it will take for Roger's investment to triple the original amount, and then the time it will take for his friend's investment to triple. We use the compound interest formula and substitute the given values to find the years needed for both scenarios.

Step-by-step explanation:

The question involves compound interest. Let's solve it step by step.

Given: Roger invested a certain amount into an account with an interest rate of 10 percent compounded annually. It will take approximately [time1] years before his investment is triple the original amount.

1. First, we need to find the time, denoted as [time1], using the compound interest formula:
2. [original amount] * (1 + [interest rate])^[time1] = [triple the original amount]
3. Next, we are told that Roger's friend invested twice as much as Roger in the same bank. Therefore, it will take [time2] years for his friend's investment to triple the original amount.
4. Again, we use the same formula to find [time2] given the new information.

Using these steps, we can calculate the approximate times it will take for both Roger and his friend's investments to triple.