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.
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