Alex and Courtney are each investing $1,200 today in a savings account. Alex will earn 4% interest compounded annually. Courtney will earn 4% simple interest. After five years Alex will have ____ more than Courtney.
A) $19.98
B) $20.13
C) $20.17
D) $20.21
E) $20.28

Question

Quizplus · Accepted Answer

Alex's investment grows according to the formula for compound interest, $A = P(1 + r)^n$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), and $n$ is the time the money is invested for in years. For Alex, $P = $1,200$, $r = 0.04$, and $n = 5$. So, Alex's amount after 5 years is $A = 1200(1 + 0.04)^5 = 1200(1.04)^5 = 1200 \times 1.2166529 = $1,459.98$.Courtney's investment grows according to the formula for simple interest, $A = P + Prn$, where $A$ is the total amount after n years, $P$ is the principal amount, $r$ is the annual interest rate (decimal), and $n$ is the time the money is invested for in years. For Courtney, $P = $1,200$, $r = 0.04$, and $n = 5$. So, Courtney's amount after 5 years is $A = 1200 + 1200 \times 0.04 \times 5 = 1200 + 240 = $1,440$.The difference between Alex's and Courtney's amounts after 5 years is $1,459.98 - 1,440 = $19.98$.

Alex and Courtney Are Each Investing $1,200 Today in a Savings