In 2 The doubling function D(r) = gives the number of years required to double your money when it is invested at interest rate r (expressed as a decimal), compounded annually. How long does it take to double In (1+r) your money at each of the following rates? (a) 6% (b) 9% (c) 18% (d) 24% (e) Round each of your answers in parts (a)-(d) to the nearest year, and compare them with these numbers 72/6, 72/9, 72/18, and 72/24. Use this evidence to state a "rule of thumb" for determining approximate doubling time without employing the function D. This rule is called the rule of 72. In 2 (a) Since the doubling function D(r) = In (1+r) uses r expressed as a decimal, convert the rate 6% to a decimal. 6% = 0.06 Substitute r=0.06 in the doubling function and evaluate. In 2 In (1+r) In 2 In (1.06 D(r) = ~ 11.90 (Type an integer or decimal rounded to the nearest hundredth as needed.)

Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
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hello for this question may someone let me know how to correctly plug in the formula to get a final answer of (11.90) as stated in the picture? (11.90)

 

1. question states: The doubling function

D(r)=ln2ln(1+r)

gives the number of years required to double your money when it is invested at interest rate r​ (expressed as a​ decimal), compounded annually. How long does it take to double your money at each of the following​ rates?

In 2
The doubling function D(r) = In (1 + r) gives the number of years required to double your money when it is invested at interest rate r (expressed as a decimal), compounded annually. How long does it take to double
your money at each of the following rates?
(a) 6%
(b) 9%
(c) 18%
(d) 24%
(e) Round each of your answers in parts (a)-(d) to the nearest year, and compare them
with these numbers 72/6, 72/9, 72/18, and 72/24. Use this evidence to state a "rule
of thumb" for determining approximate doubling time without employing the
function D. This rule is called the rule of 72.
In 2
(a) Since the doubling function D(r)= In (1 + r) uses r expressed as a decimal, convert the rate 6% to a decimal.
6% = 0.06
Substitute r=0.06 in the doubling function and evaluate.
In 2
In (1+r)
In 2
In (1.06)
D(r) =
~ 11.90|
(Type an integer or decimal rounded to the nearest hundredth as needed.)
It will take approximately 11.90 years at a rate of 6% to double the invested money.
In 2
Transcribed Image Text:In 2 The doubling function D(r) = In (1 + r) gives the number of years required to double your money when it is invested at interest rate r (expressed as a decimal), compounded annually. How long does it take to double your money at each of the following rates? (a) 6% (b) 9% (c) 18% (d) 24% (e) Round each of your answers in parts (a)-(d) to the nearest year, and compare them with these numbers 72/6, 72/9, 72/18, and 72/24. Use this evidence to state a "rule of thumb" for determining approximate doubling time without employing the function D. This rule is called the rule of 72. In 2 (a) Since the doubling function D(r)= In (1 + r) uses r expressed as a decimal, convert the rate 6% to a decimal. 6% = 0.06 Substitute r=0.06 in the doubling function and evaluate. In 2 In (1+r) In 2 In (1.06) D(r) = ~ 11.90| (Type an integer or decimal rounded to the nearest hundredth as needed.) It will take approximately 11.90 years at a rate of 6% to double the invested money. In 2
Expert Solution
Step 1

Any sum infused to earn returns or create wealth is regarded as an investment. Every investment earns a specified return each period. Using this return rate, an investor can estimate in what duration the desired accumulated investment is earned. There are multiple methods and techniques that can be employed to determine the time period. The duration function and rule of 72 are among them.

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hi im looking at the solution above and have a quuestion-im a little
puzzled on exactly how i should be plugging in the numbers
for example, the chart liists Time (ln2/(ln(1+r)) but how exactly should i type this in my calculator
to get =l3/J3? maybe im overthinking it

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