SOLUTION: A loan of $26000 is made at 3.5% interest, compounded annually. After how many years will the amount due reach $41000 or more? Write the smallest possible whole number answer.

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A loan of $26000 is made at 3.5% interest, compounded annually. After how many years will the amount due reach $41000 or more? Write the smallest possible whole number answer.      Log On


   

Question 1177564: A loan of $26000 is made at 3.5% interest, compounded annually. After how many years will the amount due reach $41000 or more? Write the smallest possible whole number answer.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
26000 * 1.035 ^ n = 41000.
n is the number of years.

divide both sides of this equation by 26000 to get:

1.035 ^ n = 41/26

take the log of both sides of this equation to get:

log(1.035^n) = log(41/26).

by one of the log laws, this is equivalent to:

n * log(1.035) = log(41/26)

divide both sides of the equation by log(1.035) and solve for n to get:

n = log(41/26) / log(1.035) = 13.24001857.

confirm by replacing n in the original equation and solving to get:

f = 26000 * 1.035 ^ 13.24001857 = 41000.

13.24001857 years is your answer.

here's a reference on laws of logs.

https://proofwiki.org/wiki/Laws_of_Logarithms