SOLUTION: Bert invests 770 dollars now, and 580 dollars in 5 years. Ten years after the first investment, the accumulated value of the combined investments is 3640 dollars. What are the poss

Question 1206523: Bert invests 770 dollars now, and 580 dollars in 5 years. Ten years after the first investment, the accumulated value of the combined investments is 3640 dollars. What are the possible effective rates of interest? (If you find more than one, list them separated by commas.
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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Bert invests 770 dollars now, and 580 dollars in 5 years.
Ten years after the first investment, the accumulated value of the combined investments is 3640 dollars.
What are the possible effective rates of interest? (If you find more than one, list them separated by commas.
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770 dollars worked and earned money for 10 years.

580 dollars worked and earned money for 5 years.

Let "r" be the unknown effective annual rate of interest.


The equation for the total money 10 years after first investment

    770*(1+r)^10 + 580*(1+r)^5 = 3640 dollars.


Denote x =  and get this quadratic equation

    770x^2 + 580x - 3640 = 0.


Solve it using the quadratic formula and get the roots, one positive  = 1.829984403  and  the other negative.

Since we are looking for positive growth coefficient, we accept the positive root and deny the negative one.


So, for now   = 1.829984403;  hence,  1 + r = 1.829984403^(1/5) = 1.128468596.

It gives  r = 0.128468596.


Round it reasonably and get  r = 0.1285 rounded,  or  r = 12.85%.   ANSWER  


CHECK.  770*1.1285^10 + 580*1.1285^5 = 3640.87  (which is good).

Solved.

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