5. Investment account 1 starts with a balance of $200 and doubles every year. Investment account 2 starts with $1,000 and increases by $100 each year.
a. How long does it take for each account to double?
b. How long does it take for each account to double again?
c. How does the growth in these two accounts compare? Explain your reasoning.
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In this exercise we will have to use the knowledge of finance to calculate the income time in this way we can say that:

a.

b.

c. The first account grows exponentially, while the second one grows at a linear rate.  

Then writing the yield formula as:

Where:

If r = 1, then it doubles every year, so we have the following expression for the first account:

a. In order for the second acount to double it needs to reach M = 2000, so we have:

b. The second account will need to reach M = 4000, therefore:

c. Since the first record of finances evolve exponentially it become larger at a faster rate distinguished to the second individual that evolve linearly over opportunity. Therefore over opportunity the first fees be apt to outdo something or someone the second individual fashionable advantage.

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a. Account 1: 1 year Account 2: 10 years

b. Account 1: 2 years Account 2: 30 years

c. The first account grows exponentially, while the second one grows at a linear rate. Therefore, over time the first account tends to surpass the second one in value.

Step-by-step explanation:

The first account can be modeled by using a compounded formula with 100% rating, since it doubles every year. The formula is shown below:

M = C*(1 + r)^t

Where M is the final amount, C is the initial amount, r is the interest rate and t is the elapsed time. If r = 1, then it doubles every year, so we have the following expression for the first account:

M = 200*(2)^t

While the second acount grows at a steady rate of $100, therefore it can be modeled by the initial amount added by the growth rate multiplied by the elapsed time as shown below:

M = 1000 + 100*t

a. The first acount take 1 year to double, since it doubles every year.

In order for the second acount to double it needs to reach M = 2000, so we have:

2000 = 1000 + 100*t

100* t = 2000 - 1000

100*t = 1000

t = 10

It will take 10 years to double.

b. The first account will double again in 1 more year, so 2 years total.

The second account will need to reach M = 4000, therefore:

4000 = 1000 + 100*t

100*t = 4000 - 1000

100*t = 3000

t = 30

It'll take 30 years total for the second account to double again.

c. Since the first account grows exponentially it grows at a faster rate in comparison to the second one that grows linearly over time. Therefore over time the first account tends to surpass the second one in value.