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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 the interest on a long-term U.S. investment is compounded continuously, how long will it take the value of an investment to double? (Give the answer correct to two decimal places.)

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Applied Calculus

7th Edition
Waner + 1 other
Publisher: Cengage Learning,
ISBN: 9781337291248
BuyFindarrow_forward

Applied Calculus

7th Edition
Waner + 1 other
Publisher: Cengage Learning,
ISBN: 9781337291248
Chapter 2.3, Problem 47E
Textbook Problem
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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 the interest on a long-term U.S. investment is compounded continuously, how long will it take the value of an investment to double? (Give the answer correct to two decimal places.)

To determine

To calculate: The time required for an investment to be double its value in U.S. if the interest is compounded continuously.

Explanation of Solution

Given Information:

The returned amount is double of its investment amount.

The interest is compounded continuously.

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 relation between growth constant and doubling time if interest is compounded continuously is,

tdk=ln2

Here, td is doubling time.

The relation between growth constant and rate of interest if interest is compounded continuously is,

k=r100

Here r is the percentage rate of interest.

Calculation:

The rate of interest in U.S. is 2.5%.

Substitute r=2.5 in the formula k=r100,

k=2

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