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Chapter 12: Problem 3

You put \(\$ 1,000\) into a savings account that pays an interest rate of 6 percent annually. How many years before your savings doubles?

Short Answer

Expert verified
It will take approximately 12 years for the savings to double.

Step by step solution

01

Set Up The Equation

Using the formula for compound interest A = P(1 + r/n)^(nt), and knowing that we want A to be double the initial deposit, we get the following equation: 2 * \$1000 = \$1000 (1 + 0.06/1)^(1t). We simplify this to 2 = (1 + 0.06)^t.
02

Solve the Equation

To solve for t, we will take the natural logarithm (ln) of both sides of the equation, which allows us to use the property of logs that brings down the exponent. It becomes ln(2) = t*ln(1.06). Divide both sides by ln(1.06) to find t. The calculation gives t ≈ 11.9.
03

Conclude

The answer means it will take approximately 12 years for the investment to double, rounding up as we can't have partial years.

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