Questions: Find the total amount in the compound interest account. 1750 is compounded daily at a rate of 10% for 5 years. Let 1 year = 365 days. (Do not round until the final answer. Then round to the nearest hundredth as needed.)

Solution Steps

To find the total amount in a compound interest account, we use the compound interest formula: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] where:

• \( A \) is the amount of money accumulated after n years, including interest.
• \( P \) is the principal amount (the initial amount of money).
• \( r \) is the annual interest rate (decimal).
• \( n \) is the number of times that interest is compounded per year.
• \( t \) is the time the money is invested for in years.

Given:

• \( P = 1750 \)
• \( r = 0.10 \)
• \( n = 365 \) (compounded daily)
• \( t = 5 \)

We will plug these values into the formula to find \( A \).

We are given the following values:

• Principal amount, \( P = 1750 \)
• Annual interest rate, \( r = 0.10 \)
• Number of times interest is compounded per year, \( n = 365 \)
• Time in years, \( t = 5 \)

The compound interest formula is: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]

Substituting the given values into the formula, we get: \[ A = 1750 \left(1 + \frac{0.10}{365}\right)^{365 \times 5} \]

Performing the calculation: \[ A = 1750 \left(1 + \frac{0.10}{365}\right)^{1825} \] \[ A \approx 2885.06 \]

Final Answer