Question 967397: A sum of $1200 is invested at an interest rate of 4.5 % compounded annually. How many years will it take until the sum exceeds $2100? Answer by jim_thompson5910(35256) (Show Source):
A = P*(1+r/n)^(n*t)
2100 = 1200*(1+0.045/1)^(1*t)
2100 = 1200*(1+0.045)^t
2100 = 1200*(1.045)^t
2100/1200 = 1.045^t
1.75 = 1.045^t
1.045^t = 1.75
log(1.045^t) = log(1.75)
t*log(1.045) = log(1.75)
t = log(1.75)/log(1.045)
t = 12.71366 (this is approximate)
It will take approximately 12.71366 years for the account to have $2100. Round up to the nearest year, 13 years, and you're guaranteed to have more than $2100 in the account.
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