Chapter 2.3, Problem 45E

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7th Edition

Stefan Waner + 1 other

ISBN: 9781337274203

Textbook Problem

**Long-Term Investments** Exercises 41-48 are based on the following table, which lists interest rates on long-term investments (based on 10-year government bonds) in several countries in 2014.^{37} **[HINT:** See Example 2.**]**

Country |
U.S. | Japan | Germany | Australia | Brazil |

Yield |
2.5% | 0.5% | 1.0% | 3.5% | 4.2% |

How long, to the nearest year, will it take an investment in Australia to double its value if the interest is compounded every 6 months?

To determine

**To calculate:** The time required for an investment to be double its value in Australia if the interest is compounded in every 6 months.

Explanation

**Given Information:**

The returned amount is double of its investment amount.

The interest is compounded every six month.

The interest rate table is,

Country | U.S. | Japan | Germany | Australia | Brazil |

Yield | 2.5% | 0.5% | 1.0% | 3.5% | 4.2% |

**Formula used:**

The formula for compound interest is,

Here,

The logarithmic relation of indices is,

**Calculation:**

The rate of interest in Australia is 3.5%.

This can be expressed in decimal form as,

The interest is compounded every six month that means interest is compounded twice a year. Therefore,

The return amount is twice of the invested amount. Therefore,

Substitute

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