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A fund offers a return of 3.5% each year. A person with 400000 wants to build up a...

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timw996 | Student, Grade 10 | Salutatorian

Posted August 31, 2013 at 6:02 PM via web

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A fund offers a return of 3.5% each year. A person with 400000 wants to build up a corpus of 1 million. For how many years should he remain invested.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted August 31, 2013 at 6:07 PM (Answer #1)

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The returns offered by the fund are 3.5% per year. Let the time that a person with $400000 has to stay invested for to accumulate $1000000 be t.

`1000000 = 400000*(1 +3.5/100)^t`

=> `2.5 = (1.035)^t`

Take the logarithm of both the sides

log 2.5 = log(1.035)^t

=> log 2.5 = t*log1.035

=> t = `log 2.5/log 1.035`

=> t `~~` 26.635

The person should stay invested for 27 years for the sum of $400000 to grow to $1 million

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