Problem

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.

Solution

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: \(\boxed{\$4052.71}\)

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