Final answer:
Sophie would have approximately $7,157 more in her account than Sydney after 20 years.
Step-by-step explanation:
To find out how much more money Sophie would have in her account than Sydney after 20 years, we need to calculate the compound amount for each account and then compare the results.
For Sophie's account, we can use the formula for continuously compounded interest: A = P * e^(rt), where A is the final amount, P is the principal (initial amount), e is the base of the natural logarithm (approximately 2.71828), r is the interest rate in decimal form, and t is the time in years.
Plugging in the values, we get A = 26,000 * e^(0.06*20).
For Sydney's account, we can use the formula for monthly compounded interest: A = P * (1 + r/n)^(nt), where A is the final amount, P is the principal, r is the interest rate in decimal form, n is the number of times the interest is compounded per year, and t is the time in years.
Plugging in the values, we get A = 26,000 * (1 + 0.05/12)^(12*20).
Calculating these values, we find that the amount in Sophie's account after 20 years is approximately $82,167, and the amount in Sydney's account is approximately $75,010.
Therefore, Sophie would have approximately $7,157 more in her account than Sydney after 20 years.