To solve this, we'll use the compound interest formula for both Aubrey and Miguel's accounts. The formula is:

$A = P \left(1 + \frac{r}{n}\right)^{nt}$

Where:

• $A$ is the amount in the account after time $t$,
• $P$ is the principal (initial investment),
• $r$ is the annual interest rate (as a decimal),
• $n$ is the number of times the interest is compounded per year,
• $t$ is the time in years.

Aubrey's Account:

Aubrey's account is compounded monthly, so:

• $P = 150$,
• $r = 6.5\% = 0.065$,
• $n = 12$ (compounded monthly),
• $t = 7$ years.

Substituting into the formula:

$A_A = 150 \left(1 + \frac{0.065}{12}\right)^{12 \times 7}$

Miguel's Account:

Miguel's account is compounded daily, so:

• $P = 150$,
• $r = 6.25\% = 0.0625$,
• $n = 365$ (compounded daily),
• $t = 7$ years.

Substituting into the formula:

$A_M = 150 \left(1 + \frac{0.0625}{365}\right)^{365 \times 7}$

Now, let’s calculate both amounts and find the difference.

I'll proceed with the calculations. Given values P = 150 t = 7

Aubrey's parameters (monthly compounding)

r_aubrey = 0.065 n_aubrey = 12

Miguel's parameters (daily compounding)

r_miguel = 0.0625 n_miguel = 365

Formula for compound interest: A = P * (1 + r/n)^(nt)

Aubrey's Account

A_aubrey = P * (1 + r_aubrey / n_aubrey)**(n_aubrey * t)

Miguel's Account

A_miguel = P * (1 + r_miguel / n_miguel)**(n_miguel * t)

Difference between Aubrey's and Miguel's final amounts

difference = A_aubrey - A_miguel

Round the difference to the nearest dollar

difference_rounded = round(difference)

A_aubrey, A_miguel, difference_roundedAfter 7 years, Aubrey would have approximately $236.14 in her account, while Miguel would have approximately $232.32. The difference between their accounts is about $4.

So, Aubrey would have $4 more than Miguel.

Would you like more details on how the calculations were done, or do you have other questions on this topic?

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Here are 5 related questions you might find interesting:

1. How does the frequency of compounding (monthly vs daily) affect the growth of an investment?
2. What would happen to the difference in final amounts if both accounts had the same interest rate?
3. How does the interest rate affect the total amount of money in the account over time?
4. What if Aubrey's account was compounded annually—how would the result change?
5. How can we calculate the interest earned in these accounts, not just the final amount?

Tip: When calculating compound interest, even small changes in the interest rate or compounding frequency can have a significant effect on the final amount, especially over longer periods.