Suppose that you put $2500 into a retirement account that grows with an interest rate of 5.25% compounded once each year. After how many years will the balance of the account be at least $15,000?

Question

mathstudent55 · Answer

You need to look up the formula for compound interest.

anonymous · Answer

Remember, interest is calculated as the starting balance multiplied by one plus the interest rate, raised to the power of n years, equals the future value 
You can solve this by setting up your problem as: 
$2,500*(1.0525^n)=$15,000 
1.0525^n=15000/2500=6 
1.0525= the nth root of 6 

n=36 years

mathstudent55 · Answer

$F = P(1 + i)^t $

$15000 = 2500(1 + 0.0525)^t $

$15000 = 2500(1.0525^t) $

$6 = 1.0525^t $

$ \log 6 = \log (1.0525^t)$

$ \log 6 = t \log 1.0525$

$ \dfrac{\log 6}{\log 1.0525} = t$

$t = 35.01699$

Since the number of years is 35.017, or approximately 35 years and 6 days, but if you can only deal with whole years, then you need 36 years.

anonymous · Answer

okay thankyou!! :)