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

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

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

Answer

Explanation:

Step1: Calculate amount for Plan A after n years

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

Step2: Calculate amount for Plan B after n years

The formula for Plan B is $A_B = 1000(1 + 0.05)^n$ using the compound - interest formula $A=P(1 + r)^n$ with $P = 1000$, $r=0.05$.

Step3: Calculate amounts after 1 year

For Plan A: $A_A(1)=1000 + 100\times1=1100$. For Plan B: $A_B(1)=1000(1 + 0.05)^1=1050$.

Step4: Calculate amounts after 2 years

For Plan A: $A_A(2)=1000+100\times2 = 1200$. For Plan B: $A_B(2)=1000(1 + 0.05)^2=1000\times1.1025 = 1102.5$.

Step5: Calculate amounts after 3 years

For Plan A: $A_A(3)=1000 + 100\times3=1300$. For Plan B: $A_B(3)=1000(1 + 0.05)^3=1000\times1.157625 = 1157.625$.

Step6: Calculate amounts after 4 years

For Plan A: $A_A(4)=1000+100\times4 = 1400$. For Plan B: $A_B(4)=1000(1 + 0.05)^4=1000\times1.21550625=1215.50625$.

Answer:

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