   Chapter 2.3, Problem 43E 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% If you invest $10,400 in Germany and the interest is compounded monthly, when, to the nearest month, will your investment be worth$20,000?

To determine

To calculate: The time a person must wait for his investment of $10400 in Germany to become$20000 if the interest is compounded monthly.

Explanation

Given Information:

The investment amount is $10400. The returned amount is$20000.

The interest is compounded monthly.

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 indexes is,

logbx=xlogb

Calculation:

The rate of interest in Germany is 1.0%.

This can be expressed in decimal form as,

r=0.01

The interest is compounded annually therefore,

m=12

Substitute A(t)=20000, P=10400, m=12 and r=0.01 in the formula A(t)=P(1+rm)mt,

20000=10400(1+0.0112)(12)t20000=10400(1.00083)12t

Divide both side by 10400,

2000010400=10400(1

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