Answer:
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.
