Problem

10. Jenna has $\$ 549.00$ in a savings account that earns $1 \%$ interest, compounded annually. To the nearest cent, how much will she have in 4 years? \[ \$ 571.29 \]

Solution

Step 1 :The problem is asking for the future value of an investment given an initial principal amount, an interest rate, and a time period. The formula for future value (FV) in the case of annual compounding is: \(FV = P * (1 + r/n)^{nt}\) where: P = principal amount (the initial amount of money), r = annual interest rate (in decimal), n = number of times that interest is compounded per year, t = time the money is invested for in years.

Step 2 :In this case, P = $549, r = 1% = 0.01, n = 1 (since it's compounded annually), and t = 4 years. We can plug these values into the formula to find the future value.

Step 3 :Substituting the given values into the formula, we get: \(FV = 549 * (1 + 0.01/1)^{1*4}\)

Step 4 :Solving the equation gives us a future value of $571.2916014900001

Step 5 :Rounding to the nearest cent, the amount Jenna will have in her savings account in 4 years is $571.29

Step 6 :Final Answer: The amount Jenna will have in her savings account in 4 years, to the nearest cent, is \(\boxed{571.29}\)

From Solvely APP
Source: https://solvelyapp.com/problems/42828/

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