Solved Question: You plan to invest in securities that pay 6%, compounded annually

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Question:

You plan to invest in securities that pay 6%, compounded annually. If you invest $5,000 today, how many years will it take for your investment to grow to $30,000?

Answer:

F = P(1 + r)t

where

P = Initial investment

r = rate of interest per annum

t = time in years

F= Maturity amount (Principal and interest compounded annually)

Given:

P = $5,000

F = $30,000

r = 6% = 0.06

Hence,

$30,000 = $5,000 (1 + 0.06) t

=> (1.06)t = 30,000 / $5,000= 6

=> log (1.06)t = log (6)

=> (t) log( 1.06) = log(6)

=> t = log(6) / log( 1.06) = 0.77815125038 / 0.02530586526 = 30.75 years

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