A college student expects to earn at least $1,000 in interest on an initial investment of $20,000. If the money is invested for one year at interest compounded quarterly, what is the least annual interest rate that would achieve the goal?

• Basically we are asked to find the minimum rate of interest for $20,000 under compound interest compounding quarterly such that the student can earn at least $1000. So, the student is expected to have at least $21,000 (Initial amount + Interest) after one full year.
  
  By compound interest formula,
  
  C.I = A * [1+(Rate in decimal/ # (Number) of Compounding)]^(# of Years * # of Compounding)
  21000 = 20000 * [1 + (R/400)]^4 ........# of compounding is 4 and rate in decimal, so R/400
  1.05 = [1 + (R/400)]^4
  Raising to power 1/4 on both sides of the above equation,
  (1.05)^(1/4) = [1 + (R/400)] ......4 * (1/4) = 1 on right side
  1.0123 ≃ 1+ (R/400) ......While using GRE calculator take square root of 1.05 twice
  0.0123 ≃ R/400
  R ≃ 4.92
  
  To earn a interest of $1000, the rate of interest should be 4.92% approx but the problem says "atleast" $1000.
  So, the rate of interest should be greater than $1000 to meet the students expectation.
  
  
• 9 years agoHelpfull: Yes(1) No(0)
• Edit: So, the rate of interest should be greater than 4.92% to meet the students expectation.
  
• 9 years agoHelpfull: Yes(0) No(0)