   Chapter 2.3, Problem 45E ### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

#### Solutions

Chapter
Section ### Finite Mathematics and Applied Cal...

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,

A(t)=P(1+rm)mt

Here, A(t) is the returned amount, P is invested amount, r is rate of interest, m the number of time in a year interest is compounded and t is time in year.

The logarithmic relation of indices is,

logbx=xlogb

Calculation:

The rate of interest in Australia is 3.5%.

This can be expressed in decimal form as,

r=0.035

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

m=2

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

A(t)=2P

Substitute A(t)=2P, m=2 and r=0.035 in the formula A(t)=P(1+rm)mt,

2P=P(1+0

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