4.) Dave deposits $\$ 3,188$ into an account earning $2.4 \%$ interest compounded daily. How much money will be in the account after 10 years? Do not round until the end. Then round to two decimals.
Answer
Rounding to two decimal places, we get the final amount of money in the account after 10 years: \(\boxed{\$4052.71}\)
Step 1 ：Let's denote the principal amount (the initial amount of money) as \( P = \$3188 \)
Step 2 ：The annual interest rate is \( r = 2.4\% = 0.024 \)
Step 3 ：The number of times that interest is compounded per unit \( t \) is \( n = 365 \) (since it is compounded daily)
Step 4 ：The time the money is invested for is \( t = 10 \) years
Step 5 ：We can calculate the amount of money in the account after 10 years using the formula for compound interest: \( A = P \cdot (1 + \frac{r}{n})^{nt} \)
Step 6 ：Substitute the given values into the formula: \( A = 3188 \cdot (1 + \frac{0.024}{365})^{365 \cdot 10} \)
Step 7 ：After calculating the above expression, we find that \( A = 4052.7103149502777 \)
Step 8 ：Rounding to two decimal places, we get the final amount of money in the account after 10 years: \(\boxed{\$4052.71}\)
