Problema Solution

the function y=1000(1.005)^x models that the value off $1000 depositat an interest in rate of 6% per year (.005 per month)x months after the deposited. How many months will it take for the account to reach %1100? Predict how many years it will take the money to be worth $1100?

Answer provided by our tutors

FIRST PART

(1+1100/100)*1000=12000=1000*(1.005)^x

If we cancel zeros, we have

12=1.005^x

Take both sides into log function,

ln12=x*ln(1.005)

then,

x=ln12/ln(1.005)=486.862~~487 months 

SECOND PART

1100=1000*(1.005)^x

Then, we have

1.1=1.005^x and by using the same method above

x=ln(1.1)/ln(1.005)=19.11~~20 months(1 year and 8 months)