Kyran was given a check for $100 by his grandmother for his birthday, but had to promise her that he would invest the money in a
bank until it had at least doubled in value. Kyran agreed, reluctantly, and found a bank where he could invest the $100 in a simple interest account that would gain 5% interest per year. If represents the number of years that Kyran will invest his money, which inequality could be used to find when he would have at least $200 in his account?
The equation for simple interest is sated as follows: A=P(1+rt), where A= The accrued amount, P=Principal invested, r=interest rate per year, and t=time in years. For the amount invested to be atleast double the amount invested (like the current scenario), the inequality would be would be A≥ P(1+rt) ---- 200≥100 (1+0.05t) ---- 2≥1+0.05t --- t≥(2-1)/0.05 --- t≥20 years
Therefore, for the amount to atleast double, $100 should be invested for atleast 20 years.
