Answer:
To determine how much money Avani would have in her account when Brianna's money has tripled in value, we need to calculate the future value of both investments.
First, let's calculate the future value of Brianna's investment. The formula for continuous compounding is given by:
A = P * e^(rt)
Where:
A is the future value
P is the principal amount (initial investment)
e is Euler's number (approximately 2.71828)
r is the interest rate
t is the time in years
In this case, Brianna invested $340 at an interest rate of 2% compounded continuously. We want to find the time it takes for her investment to triple in value. Let's denote this time as t.
3P = P * e^(0.02t)
Dividing both sides by P, we get:
3 = e^(0.02t)
Taking the natural logarithm of both sides, we have:
ln(3) = 0.02t
Solving for t, we find:
t ≈ ln(3) / 0.02 ≈ 51.97 years
Therefore, it would take approximately 51.97 years for Brianna's investment to triple in value.
Now, let's calculate the future value of Avani's investment using compound interest formula:
A = P * (1 + r/n)^(nt)
Where:
A is the future value
P is the principal amount (initial investment)
r is the interest rate
n is the number of times interest is compounded per year
t is the time in years
In this case, Avani invested $340 at an interest rate of 17% compounded annually. We want to find the future value after 51.97 years.
A = 340 * (1 + 0.17/1)^(1*51.97)
Calculating this, we find:
A ≈ 340 * (1.17)^(51.97) ≈ $13,154.74
Therefore, Avani would have approximately $13,155 in her account when Brianna's money has tripled in value.
Answer: Avani would have approximately $13,155 in her account when Brianna's money has tripled in value.
Explanation: