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

adita has two options for how to invest $1,000.\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.\nwhich statement is true?\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.\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.\nwhich statement is true?\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 value of Plan A after (n) years

The value (V_A) of Plan A after (n) years with an initial investment of (P = 1000) and an annual payment of (a=100) is given by (V_A=1000 + 100n).

Step2: Calculate value of Plan B after (n) years

The value (V_B) of Plan B after (n) years with an initial investment of (P = 1000) and an annual - interest rate (r = 0.05) compounded annually is given by the compound - interest formula (V_B=1000(1 + 0.05)^n).

Step3: Calculate values for (n = 1)

For (n = 1): (V_A=1000+100\times1=1100) (V_B=1000(1 + 0.05)^1=1000\times1.05 = 1050) So Plan A is worth more than Plan B after 1 year.

Step4: Calculate values for (n = 2)

(V_A=1000+100\times2=1200) (V_B=1000(1 + 0.05)^2=1000\times1.05^2=1000\times1.1025 = 1102.5) So Plan A is worth more than Plan B after 2 years.

Step5: Calculate values for (n = 3)

(V_A=1000+100\times3=1300) (V_B=1000(1 + 0.05)^3=1000\times1.05^3=1000\times1.157625 = 1157.625) So Plan A is worth more than Plan B after 3 years.

Step6: Calculate values for (n = 4)

(V_A=1000+100\times4=1400) (V_B=1000(1 + 0.05)^4=1000\times1.05^4=1000\times1.21550625 = 1215.50625) So Plan A is worth more than Plan B after 4 years.

Answer:

None of the given statements are true.