To solve this problem, we need to use the formula for compound interest:

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

Where:

• $A$ is the amount in the account after interest.
• $P$ is the principal (initial amount), which is $1,900.
• $r$ is the annual interest rate, which is 4.5%, or 0.045 as a decimal.
• $t$ is the time in years, which is 2 years.
• $n$ is the number of times the interest is compounded per year. Since it’s compounded daily, $n = 365$.

Plugging the values into the formula:

$A = 1900 \left(1 + \frac{0.045}{365}\right)^{365 \times 2}$

Let's calculate that step-by-step:

1. $\frac{0.045}{365} = 0.0001232876712$
2. Adding 1 to this gives $1 + 0.0001232876712 = 1.0001232876712$
3. Now, raise this value to the power of $365 \times 2 = 730$: $(1.0001232876712)^{730} = 1.093148768$
4. Finally, multiply this by the principal $P = 1900$: $A = 1900 \times 1.093148768 = 2077.98$

Answer:

The amount in the account after 2 years, compounded daily, is approximately $2,077.98.

Would you like more details or have any questions?

Here are 5 related questions you might be interested in:

1. How does the number of compounding periods affect the total amount?
2. What would happen if the interest rate increased to 5%?
3. How would the result change if compounded monthly instead of daily?
4. Can you explain the difference between simple and compound interest?
5. What happens if the compounding is continuous rather than daily?

Tip: The more frequently interest is compounded, the greater the final amount, even with the same interest rate.