SOLUTION: At 4 % interest compounded monthly, how long will it take to turn a hundred dollars into a million dollars? Round your answer to two decimal places

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Question 931886: At 4 % interest compounded monthly, how long will it take to turn a hundred dollars into a million dollars?
Round your answer to two decimal places
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We will use A+=+P%2A%281%2Br%2Fn%29%5E%28n%2At%29 where

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A = 10^6 (equivalent to 1 million)
P = 100
r = 0.04
n = 12
t = unknown (we're solving for this)


A is the final amount, P is the initial amount
r is the interest rate as a decimal
n is the compounding frequency
t is the time in years

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Plug in the given values above and solve for t.


A+=+P%2A%281%2Br%2Fn%29%5E%28n%2At%29


10%5E6+=+100%2A%281%2B0.04%2F12%29%5E%2812%2At%29


10%5E6+=+100%2A%281.0033333333%29%5E%2812%2At%29 Use a calculator here


%2810%5E6%29%2F%28100%29+=+%281.0033333333%29%5E%2812%2At%29


10%5E4+=+%281.0033333333%29%5E%2812%2At%29


log%28%2810%5E4%29%29+=+log%28%28%281.0033333333%29%5E%2812%2At%29%29%29 Apply logs to both sides (needed to extract out the exponent)


4%2Alog%28%2810%29%29+=+12t%2Alog%28%281.0033333333%29%29


4%2Alog%28%2810%29%29+=+t%2A12log%28%281.0033333333%29%29


%284%2Alog%28%2810%29%29%29%2F%2812log%28%281.0033333333%29%29%29+=+t


230.642062936+=+t Use a calculator here


t+=+230.642062936


t+=+230.64 Round to 2 decimal places


It will take approximately 230.64 years (definitely not within the person's lifetime)
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