Problem

Sheba opened a retirement account with 36,500$. Her account grew at a rate of $7 \%$ per year compounded annually. She made no deposits or withdrawals on the account. What was the account worth, at the end of 2 years, to the nearest dollar?

Solution

Step 1 :Translate the problem into the formula for future value in compound interest: \(FV = P * (1 + r/n)^{nt}\)

Step 2 :Substitute the given values into the formula: \(FV = 36500 * (1 + 0.07/1)^{1*2}\)

Step 3 :Simplify the expression inside the parentheses: \(FV = 36500 * (1.07)^2\)

Step 4 :Calculate the future value to the nearest dollar: \(FV = 41789\)

Step 5 :Final Answer: The account was worth \(\boxed{41789}\) at the end of 2 years, to the nearest dollar.

From Solvely APP
Source: https://solvelyapp.com/problems/8536/

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