SOLUTION: M wishes to determine how long it will take an initial deposit of $10,000 to double. Required: a) If M earns 10% annual interest on the deposit, how long will it take for him to

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Question 1201799: M wishes to determine how long it will take an initial deposit of $10,000 to double.
Required:
a) If M earns 10% annual interest on the deposit, how long will it take for him to double his money?
b) How long will it take if he earns only 7% annual interest?
c) Reviewing your findings in parts a and b, indicate what relationship exists between the interest rate and the amount of time it will take M to double his money.

Found 2 solutions by ikleyn, mananth:
Answer by ikleyn(52805)   (Show Source): You can put this solution on YOUR website!
M wishes to determine how long it will take an initial deposit of $10,000 to double.
Required:
a) If M earns 10% annual interest on the deposit, how long will it take for him to double his money?
~~~~~~~~~~~~~~~~~~~

For the amount of $10,000, compounded yearly, the future value formula is

    Future Value = 

where n is the number of years.



Therefore, our equation to find "n" is

    20000 = 


Divide both sides by 10000

     = ,

or, reducing left side,

    2 = .


To solve this equation, take logarithm base 10 of both sides

    log(2) = n*log(1.1)


and find "n" using your calculator

    n =  = 7.27  years.


Finally, round this value 7.27 to the nearest greater integer 8 (8 years),

in order for the bank was in position to make the last compounding.


ANSWER. 8 years.

Solved.

Do other part similarly: continue by the same way.

-------------------

To see many other similar  (and different)  solved problems,  look into the lesson
    - Problems on discretely compound accounts
in this site,  and learn the subject from there.


After reading this lesson,  you will tackle such problems on your own without asking for help from outside.


Happy learning (!)


///////////////////


Hello, when you see the answer from other tutor/tutors to this problem,
not rounded to the whole  (integer)  number of years,  this answer  (or such answer)  is  INCORRECT.

The problem  ASSUMES  that you round the decimal number of years to the closest greater  INTEGER  number of years.

Any reasonable person,  solving such problems,  should understand it as clear
as he  (or she)  does understand that   2 x 2  is  4.



Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
Present value $10000
Future value double = 20000
rate = 10%
Present Value=Future Value/(1+r)n
10000 = 20000/(1+0.1)^n
(1.1)^n = 20000/10000
1.1^n = 2
n = log2/log1.1
= 7.2725 years
How long will it take if he earns only 7% annual interest?
same formula same method 10.2448 years
it is clear you can deduce


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