Final answer:
We can solve this problem by first setting up an equation for Jayden's investment and then using the formula for compound interest to calculate Paisley's investment.
Step-by-step explanation:
To find out how much money Paisley would have in her account when Jayden's money has tripled in value, we need to determine the time it takes for Jayden's money to triple in value and then calculate the amount of money Paisley would have in her account at that time.
Let's start with Jayden's investment. If his money triples in value, it means that the final amount is three times the initial amount. Let x be the initial amount. So, the final amount would be 3x.
Now, let's calculate the time it takes for Jayden's money to triple in value. We can use the formula:
Next, we can use the formula for compound interest:
A = P(1 + R/n)^(nt)
In the case of Paisley, she invested $16,000 with an interest rate of 8 3/8% compounded monthly. So, P = $16,000, R = 8 3/8% = 0.08375, n = 12 (number of compounding periods per year), and t = x+4 years (the time it takes for Jayden's money to triple).
Therefore, the equation becomes:
3x = 16000(1 + 0.08375/12)^(12(x+4))
Solving this equation will give us the value of x, which is the initial amount of money Jayden invested. Once we have x, we can calculate how much money Paisley would have in her account at the same time using the formula for compound interest.
To find the nearest dollar, we can round the final amount to the nearest dollar.