SOLUTION: dani invests 200 dollars at a rate of y% per year compound interest. at the end of 10 years the value of her investment is 256 dollars. Calculate the value of y, correct to 1 decim

Question 1115217: dani invests 200 dollars at a rate of y% per year compound interest. at the end of 10 years the value of her investment is 256 dollars. Calculate the value of y, correct to 1 decimal place
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
investment $200
rate of y% per year
compound annually
10 years
------------------------
200(1+y)^10 = 256
Let's divide both sides by 200 and we end up with:
(1+y)^10 = 256/200 simplify the right side, divide the top/bottom by 8:
(1+y)^10 = 32/25
Now to get rid of the exponent I am going to raise both sides to the inverse of 10 (you can do it with square roots but I find this easier):
((1+y)^10)^1/10 = (32/25)^1/10
On the right, divide 32/25. On the left, the power and its inverse cancel one another and we get:
1+y = 1.28^(1/10)
Now, let's make life easy. 1/10 = 0.1:
1+y = 1.28^0.1
= 1+y = 1.025
subtract 1 from both sides:
y = 0.025
since you need percent: 0.025*100= 2.5%
========================================
Check:
200(1+0.025)^10 = 256
= 200(1.28) = 256 multiply on the left and prove that it is CORRECT.
Happy learning,
John

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