Final answer:
To determine how much money Madeline would have in her account when Andres's money has tripled in value, we need to calculate the number of compounding periods it would take for Andres's money to triple. By plugging in the values into the compound interest formula and using logarithms, we can find the number of quarters it would take for Andres's money to triple. We can then use the formula for continuous compounding to calculate the future amount in Madeline's account.
Step-by-step explanation:
To determine how much money Madeline would have in her account when Andres's money has tripled in value, we need to calculate the number of compounding periods it would take for Andres's money to triple. Given that Andres invested $2,400 with an interest rate of 7(3)/(8)% compounded quarterly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A is the future amount
P is the principal amount ($2,400)
r is the annual interest rate expressed as a decimal (0.078125)
n is the number of times interest is compounded per year (4 for quarterly)
t is the number of years (unknown)
We can solve for t by plugging in the values and rearranging the formula:
3P = P(1 + r/n)^(nt)
Using logarithms, we can solve for t, which represents the number of quarters it would take for Andres's money to triple. Once we have t, we can calculate the future amount in Madeline's account using the formula for continuous compounding:
A = Pe^(rt)
where:
e is Euler's number (approximately 2.71828)
P is the principal amount ($2,400)
r is the annual interest rate expressed as a decimal (0.075)
t is the number of years (found in the previous step)
By plugging in the values, we can calculate how much money Madeline would have in her account when Andres's money has tripled.