   Chapter 2.3, Problem 41E 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% Assuming that you invest $10,000 in the United States, how long (to the nearest year) must you wait before your investment is worth$15,000 if the interest is compounded annually?

To determine

To calculate: The time a person must wait for his investment of $10000 in United States to become$15000 if the interest is compounded annually.

Explanation

Given Information:

The investment amount is $10000. The returned amount is$15000.

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 United States is 2.5%.

This can be expressed in decimal form as,

r=0.025

The interest is compounded annually therefore,

m=1

Substitute A(t)=15000, P=10000, m=1 and r=0.025 in the formula A(t)=P(1+rm)mt,

15000=10000(1+0

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