SOLUTION: A bank account starts with $700 and earns an annual interest rate of 6%, compounded monthly. What will the balance be after 2 years? B= 789.01 (I know how to solve this part)

Algebra ->  Finance -> SOLUTION: A bank account starts with $700 and earns an annual interest rate of 6%, compounded monthly. What will the balance be after 2 years? B= 789.01 (I know how to solve this part)      Log On


   

Question 1136980: A bank account starts with $700 and earns an annual interest rate of 6%, compounded monthly.
What will the balance be after 2 years?
B= 789.01 (I know how to solve this part)
How long will it take the balance to reach $1000?
t= ? (I'm having trouble solving this part. Any help is appropriated. Thank you!)
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


For the part you solved, you know the amount of time and you want to know the final balance:

700%281%2B.06%2F12%29%5E%28%282%2A12%29%29+=+700%281.005%29%5E24+=+789.01

So you did that part right.

For the other part, the formula is the same; but now the final value is known and the amount of time is not:

700%281.005%29%5Et+=+1000

With the unknown in an exponent, you need to use logarithms to solve the problem.

1.005%5Et+=+1000%2F700+=+10%2F7
t%2Alog%28%281.005%29%29+=+log%28%2810%2F7%29%29
t+=+log%28%2810%2F7%29%29%2Flog%28%281.005%29%29

Use a calculator...; and remember the answer you get is in months.