To find the value of the account after 3 years with daily compounding interest, we can use the compound interest formula:

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

Where:

• $A$ is the amount in the account after time $t$,
• $P$ is the principal amount (initial deposit),
• $r$ is the annual interest rate (in decimal form),
• $n$ is the number of times the interest is compounded per year (for daily compounding, $n = 365$),
• $t$ is the time the money is invested or borrowed for, in years.

Given:

• $P = 30,000$,
• $r = 0.0225$ (2.25% as a decimal),
• $n = 365$ (daily compounding),
• $t = 3$ years.

Now, we substitute the values into the formula:

$A = 30,000 \left( 1 + \frac{0.0225}{365} \right)^{365 \times 3}$

Let’s calculate the value:

$A = 30,000 \left( 1 + 0.00006164 \right)^{1095}$

$A = 30,000 \times (1.00006164)^{1095}$

$A \approx 30,000 \times 1.072486$

$A \approx 32,174.58$

Thus, the value of the account after 3 years is approximately $32,174.58.

Would you like more details on how the formula works, or have any questions on this topic?

Related Questions:

1. What would the value of the account be after 5 years?
2. How does compounding frequency (daily, monthly, etc.) affect the account balance over time?
3. How do you convert an interest rate from a percentage to a decimal?
4. What would happen to the account value if the interest rate were higher (say, 3%)?
5. How does compound interest compare to simple interest in terms of growth?

Tip: When using compound interest formulas, always remember that the more frequently interest is compounded, the greater the final amount, due to the effects of earning "interest on interest."