Question

If you put $100 in a bank account that pays you 10% interest, compounded annually, how many years would it take you to attain a balance of more than $200, assuming no withdrawals were made?

Answer 1

Total amount = P(1 + r/100)^n
200 < 100(1 + 10/100)^n
200 < 110^n
log110^n > log200
n x log110 > log200
n > log200/log110
n > 1.13 (to 3 significant figures)

It would take more than 1.13 years for me to attain a balance of more than $200, assuming no withdrawals were made.