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23. If you invest $100 per month in the stock market, how long will it be before your account has $1,000,000 in it? Assume th
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Answer #1

Amount Invested each month = P = $100

Monthly interest Rate = r = 0.12/12 = 0.01

Let the number of months be n

Future Value required = FV = $1000000

Hence, FV = P(1+r)n-1 +....+ P(1+r)2 + P(1+r) + P = P[(1+r)n -1]/r

=> 1000000 = 100[(1+0.01)n -1]/0.01

=> (1+0.01)n = 1 + 1000000*0.01/100 = 101

=> n = ln(101) / ln (1.01) = 463.82

Hence, it will take 463.82 months for the account to reach $1000000

463.82 months = 463.81/12 = 38.65 years

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