SOLUTION: 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?

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): You can put this solution on YOUR website!
Plug in the given values and use logs to isolate t.

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.
RELATED QUESTIONS
If $250.00 is invested at 5% compounded annually, how many years will it take until your... (answered by ewatrrr)

A principal of $3000 is invested at 5.5% interest, compounded annually. How many years... (answered by mananth)

A principal of $3500 is invested at 6.5% interest, compounded annually. How many years... (answered by reviewermath)

A principal of $3800 is invested at 6.25% interest, compounded annually. How many years... (answered by stanbon)

A principal of $1300 is invested at 8.75% interest, compounded annually. How many (answered by nerdybill)

A principal of $1400 is invested at 6% interest, compounded annually. How many years will (answered by addingup)

How long will it take a sum of money to treble if it is invested at 15% interest... (answered by Fombitz)

principal of $3500 is invested at 5.75% interest, compounded annually. How many... (answered by greenestamps)

how many years will it take for an amount of money to double when it is compounded... (answered by nerdybill,mananth)