Questions: This set of problems is designed to be calculated using the Excel or financial calculator. You can also use algebraic formulas. Do not use financial tables to calculate these problems. Question 1 (1 point) If you invest 20,848 today at an interest rate of 4.04 percent, compounded daily, how much money will you have in your savings account in 14 years? Round the answer to two decimal places.

Solution Steps

We start by identifying the variables needed for the compound interest formula:

• \( P = 20848 \) (the principal amount)
• \( r = 0.0404 \) (the annual interest rate)
• \( n = 365 \) (the number of times interest is compounded per year)
• \( t = 14 \) (the number of years the money is invested)

We apply the compound interest formula:

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

Substituting the identified variables into the formula gives:

\[ A = 20848 \left(1 + \frac{0.0404}{365}\right)^{365 \times 14} \]

We calculate the value of \( A \) using the expression derived in Step 2. After performing the calculations, we find:

\[ A \approx 36701.83 \]

This represents the total amount in the savings account after 14 years, rounded to two decimal places.

Final Answer