Final answer:
To find the difference between Leah and Brianna's accounts after 19 years, we can calculate the amounts using the formulas for compound interest. For Leah's account, we use the formula for compound interest with monthly compounding. For Brianna's account, we use the formula for continuous compounding. Finally, we subtract Brianna's amount from Leah's amount to find the difference.
Step-by-step explanation:
To calculate the amount of money Leah would have in her account after 19 years, we can use the formula for compound interest:
A = P(1 + r/n)nt
Where A is the final amount, P is the principal (initial investment), r is the interest rate (in decimal form), n is the number of times interest is compounded per year, and t is the number of years.
For Leah's account, P = $48,000, r = 7 (5/8)% = 7.625% = 0.07625, and n = 12 (compounded monthly). Plugging in these values, we get:
A = $48,000(1 + 0.07625/12)(12)(19)
Calculating this expression will give us the amount of money Leah would have after 19 years.
For Brianna's account, since it is compounded continuously, we can use the formula:
A = Pert
Where A is the final amount, P is the principal, r is the interest rate, and t is the number of years.
For Brianna's account, P = $48,000, r = 7(1/4)% = 7.25% = 0.0725, and t = 19. Plugging in these values, we get:
A = $48,000e(0.0725)(19)
Calculating this expression will give us the amount of money Brianna would have after 19 years.
To find the difference between Leah and Brianna's accounts, we can subtract the amount in Brianna's account from the amount in Leah's account.