adita has two options for how to invest $1,000.\n\nplan a: put the $1,000 in an account that pays $100 per…

adita has two options for how to invest $1,000.\n\nplan a: put the $1,000 in an account that pays $100 per year.\nplan b: put the $1,000 in an account that pays 5 percent interest per year.\n\nwhich statement is true?\n\n○ plan a will be worth more than plan b after two years.\n○ plan a will be worth the same amount as plan b after one year.\n○ plan b will be worth more than plan a after three years.\n○ plan b will be worth more than plan a after four years.

adita has two options for how to invest $1,000.\n\nplan a: put the $1,000 in an account that pays $100 per year.\nplan b: put the $1,000 in an account that pays 5 percent interest per year.\n\nwhich statement is true?\n\n○ plan a will be worth more than plan b after two years.\n○ plan a will be worth the same amount as plan b after one year.\n○ plan b will be worth more than plan a after three years.\n○ plan b will be worth more than plan a after four years.

Answer

Explanation:

Step1: Calculate the value of Plan A after n years

The formula for the value of Plan A is $V_A=1000 + 100n$, where $n$ is the number of years.

Step2: Calculate the value of Plan B after n years

The formula for compound - interest is $V = P(1 + r)^n$, where $P = 1000$ (principal amount), $r=0.05$ (interest rate), and $n$ is the number of years. So, $V_B = 1000(1 + 0.05)^n=1000\times1.05^n$.

Step3: Calculate the value after 1 year

For Plan A: $V_A(1)=1000 + 100\times1=1100$. For Plan B: $V_B(1)=1000\times1.05^1 = 1050$.

Step4: Calculate the value after 2 years

For Plan A: $V_A(2)=1000+100\times2 = 1200$. For Plan B: $V_B(2)=1000\times1.05^2=1000\times1.1025 = 1102.5$.

Step5: Calculate the value after 3 years

For Plan A: $V_A(3)=1000 + 100\times3=1300$. For Plan B: $V_B(3)=1000\times1.05^3=1000\times1.157625 = 1157.625$.

Step6: Calculate the value after 4 years

For Plan A: $V_A(4)=1000+100\times4 = 1400$. For Plan B: $V_B(4)=1000\times1.05^4=1000\times1.21550625 = 1215.50625$.

Answer:

Plan A will be worth more than plan B after two years.