SOLUTION: You have two investments. One you put $5,000 into that returns 10% compounded quarterly. The other investment you $10,000 into that returns 5% compounded quarterly. Will these two

Question 1090057: You have two investments. One you put $5,000 into that returns 10% compounded quarterly. The other investment you $10,000 into that returns 5% compounded quarterly. Will these two investments ever be worth the same amount? If so, in what month?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
one is 5000(1+.025)^4n
other is 10000(1+.0125)^4n
this is equivalent to (1.025)^n and 2(1.0125)^n
The first should catch the second at some point.
set them equal.
10000(1.0125)^n=5000(1.025)^n
2(1.0125)^n=1.025^n
2=(1.025/1.0125)^n
ln both sides
ln2= n ln (1.025/1.0125)=n*0.012227
0.693=0.012227 n
n=56.49 quarterly compoundings or just over 14 years or 168 months

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