Suppose Joan has $5,000 to invest. The banks are offering 3.10% interest. Bank A compounds interest continuously, while Bank B compounds interest semiannually. Answer these questions regarding which bank Joan should invest her money in, to accrue the greatest return.

How much would Joan's investment be worth after 20 years at Bank A?

and Bank B?

I got $ 9,294.64 for the both of them, but that seems a little suspicious

To calculate the future value of an investment, we can use the formula:

A = P * e^(rt)

Where:
A = the future value of the investment
P = the initial principal (Joan's investment)
e = Euler's number (approximately 2.71828)
r = the interest rate (in decimal form)
t = the time period in years

For Bank A, since it compounds interest continuously, we can use the formula where r is the annual percentage rate (APR) divided by 100:

r = APR / 100

For Bank B, since it compounds interest semiannually, we need to adjust the interest rate and time period. We can calculate the adjusted interest rate (r') and time period (t') as:

r' = APR / (2 * 100)
t' = 2 * t

Let's calculate the future value for Joan's investment in each bank.

For Bank A:
P = $5,000
APR = 3.10%
t = 20 years

First, calculate the annual interest rate (r) for Bank A:
r = 3.10 / 100 = 0.031

Now, substitute the values in the formula:
A = 5000 * e^(0.031 * 20)

Calculating this, we get:
A ≈ $9,812.37

For Bank B:
P = $5,000
APR = 3.10%
t = 20 years

First, calculate the adjusted interest rate (r') for Bank B:
r' = 3.10 / (2 * 100) = 0.0155

Next, calculate the adjusted time period (t') for Bank B:
t' = 2 * 20 = 40 years

Now, substitute the values in the formula:
A = 5000 * (1 + r')^(t')

Calculating this, we get:
A ≈ $9,898.33

Therefore, after 20 years, Joan's investment at Bank A would be worth approximately $9,812.37, while her investment at Bank B would be worth approximately $9,898.33. So, the investment in Bank B would yield a slightly higher return.