SOLUTION: How long does $1000 have to be deposited into a savings account at the end of each month to accumulate to $36 000 if interest is 6.4% compounded monthly?

Question 1207351: How long does $1000 have to be deposited into a savings account at the end of each month to accumulate to $36 000 if interest is 6.4% compounded monthly?
Answer by ikleyn(52792) (Show Source): You can put this solution on YOUR website!
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How long does $1000 have to be deposited into a savings account at the end of each month
to accumulate to $36,000 if interest is 6.4% compounded monthly?
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Use the formula for an Ordinary Annuity saving account compounded monthly 


    FV = 


where FV is the future value, P is the payment at the end of each month, 
r is the interest rate per year expressed as decimal, 
n is the number of monthly deposits (of months).


So, we need to find " n " from this equation


     =  =  = 36, 

     = . 


Rewrite it in this form

     = 0.192,

     = 1 + 0.192 = 1.192.


Take logarithm base 10 of both sides

    n*log(1+0.064/12) = log(1.192)


and calculate  

     n =  = 33.01885 months.


Round it to the closest greater month, which is 34 months. 
34 months is the same as 2 years and 10 months.


ANSWER.  34 months, or 2 years and 10 months.

Solved.

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On ordinary annuity saving plan, see my lessons in this site

- Ordinary Annuity saving plans and geometric progressions
- Solved problems on Ordinary Annuity saving plans

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