SOLUTION: amira invests $100 in an account that gain 3% interest every year. Ruby invests $50 into an account that earns 2% interest every half year. In how many years will the accounts have

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: amira invests $100 in an account that gain 3% interest every year. Ruby invests $50 into an account that earns 2% interest every half year. In how many years will the accounts have      Log On


   



Question 1140511: amira invests $100 in an account that gain 3% interest every year. Ruby invests $50 into an account that earns 2% interest every half year. In how many years will the accounts have the same value?
Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


100%281.03%5Ex%29+=+50%281.02%5E%282x%29%29
100%281.03%5Ex%29+=+50%281.02%5E2%29%5Ex
100%281.03%5Ex%29+=+50%281.0404%5Ex%29
2%281.03%5Ex%29+=+1.0404%5Ex
1.0404%5Ex%2F1.03%5Ex+=+2
%281.0404%2F1.03%29%5Ex+=+2
x%2Alog%28%281.0404%2F1.03%29%29+=+log%28%282%29%29
x+=+log%28%282%29%29%2Flog%28%281.0404%2F1.03%29%29

Use a calculator....

Or with a good graphing calculator like the TI83, you can simply graph 100%281.03%5Ex%29 and 50%281.02%5E%282x%29%29 and find their intersection.