SOLUTION: The Question: $6734 is deposited into a savings account at 4% interest, compounded monthly. To the nearest year, how long will it take for the account balance to reach $1,000,000?

Question 992185: The Question: $6734 is deposited into a savings account at 4% interest, compounded monthly. To the nearest year, how long will it take for the account balance to reach $1,000,000?
The question is multiple choice, but when I work it out my answer fits none of the choices.
My solution:
A = P (1 + r/m)^n
A = 1,000,000
P = 6,734
r = 4% = 0.04
m = 12
n = 12n
1,000,000 = 6734 (1 + 0.04/12)^12n
I divide both sides by 6734 cancelling out the number on the right side leaving me with:
1,000,000/6734 = (1 + 0.04/12)^12n
148.500 = (1.003)^12n
I take the LOG of both sides.
LOG 148.500 = 12n LOG (1.003)
I divide both sides by 12 LOG (1.003) isolating n. Leaving me with:
n = LOG 148.500/12 LOG (1.003)
n = 139.11
My answer: Approximately 139 years.
Am I doing something wrong? I just started learning about LOG. Maybe I'm working the problem out wrong.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

You are doing the problem correctly, but I suspect you have an arithmetic error.

Check your calculator work; you should get 125 and change.

I figured out where you went wrong. You rounded off too soon when you calculated

Using 1.003 in the calculation gives you 139 and change. Using 1.00333... to as many digits as your calculator will keep gives you 125.22+. Object lesson: Never round off until the last step in a multi-step calculation.

John

My calculator said it, I believe it, that settles it

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