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):
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