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A dollar invested today grows to $1.10 in six months. What is the effective annual rate if you deposit your money in a bank for one year? a. none of them. b. 5% c. 21% d. 10% e. 20%

Question

A dollar invested today grows to $1.10 in six months. What is the effective annual rate if you deposit your money in a bank for one year?

a. none of them.

b. 5%

c. 21%

d. 10%

e. 20%

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Solution

The correct answer is c. 21%.

Here's the step-by-step calculation:

  1. The growth rate for six months is 10% (from 1to1 to 1.10).

  2. Since the question asks for the effective annual rate, we need to consider the compounding effect.

  3. If you invest 1,itbecomes1, it becomes 1.10 after six months. If you reinvest that 1.10foranothersixmonths,itgrowsbyanother101.10 for another six months, it grows by another 10%, which means it becomes 1.10 * 1.10 = $1.21 at the end of one year.

  4. Therefore, the effective annual rate is 21% (from 1to1 to 1.21).

This problem has been solved

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