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Chapter 17: Problem 70

If \(\$ 1,000\) is deposited in a savings account that pays 6 percent annual interest and all the interest is left in the account, what is the account balance after three years? a) \(\$ 840\) c) \(\$ 1,180\) b) \(\$ 1,000\) d) \(\$ 1,191\)

Short Answer

Expert verified
Answer: (d) $1,191

Step by step solution

01

Understand the compound interest formula

The formula for compound interest is: \(A = P(1 + r/n)^{nt}\) Where: - \(A\) is the account balance after t years - \(P\) is the principal amount (initial deposit) - \(r\) is the annual interest rate (in decimal form) - \(n\) is the number of times interest is compounded per year - \(t\) is the number of years In this case, the interest is compounded annually, so \(n = 1\). We're also given \(P = \$1,000\), \(r = 6\% = 0.06\), and \(t = 3\) years.
02

Substitute the given values into the formula

Now, substitute the values into the compound interest formula: \(A = 1000(1 + 0.06/1)^{1 * 3}\)
03

Solve for the account balance (A)

Simplify and calculate the account balance: \(A = 1000(1 + 0.06)^{3}\) \(A = 1000(1.06)^{3}\) \(A = 1000(1.191016)\) \(A = \$1,191\)
04

Choose the correct answer

The account balance after three years is \(\$1,191\), which corresponds to option (d). Therefore, the correct answer is: \(\boxed{\text{(d)}\ \$1,191}\).

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