To solve this problem, we need to first determine how long it will take for Justin's money to triple in value. We can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the final amount
P = the principal (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
For Justin, we have:
P = $940
r = 0.07625
n = 12 (monthly compounding)
t = unknown
We want to solve for t when A = 3P = $2820. We can rearrange the formula and plug in the values:
A = P(1 + r/n)^(nt)
3P = P(1 + r/n)^(nt)
3 = (1 + 0.07625/12)^(12t)
ln(3) = 12t * ln(1 + 0.07625/12)
t = ln(3) / (12 * ln(1 + 0.07625/12))
t ≈ 15.8 years
So it will take Justin about 15.8 years for his money to triple in value.
Now we can use the same formula to find how much money Hailey will have in her account after 15.8 years:
P = $940
r = 0.0825
n = 4 (quarterly compounding)
t = 15.8
A = P(1 + r/n)^(nt)
A = $940(1 + 0.0825/4)^(4*15.8)
A ≈ $3501
Therefore, Hailey will have about $3,501 in her account when Justin's money has tripled in value