Answer:
Account B earns more interest.
After 20 years, account B will have earned $171.89 more.
Step-by-step explanation:
Let's calculate the total for each account.
Account A:
Account A earns simple interest. We know that the principal value is $2000 and the interest rate is 2% or 0.02. We can use the simple interest formula:
[tex]A=P(1+rt)[/tex]
Where A is the future value, P is the principal, r is the rate, and t is the time in years.
So, let's substitute 2000 for P, 0.02 for r, and 20 for t. This yields:
[tex]A=2000(1+0.02(20))[/tex]
Multiply and add:
[tex]A=2000(1+0.4)=2000(1.4)[/tex]
Multiply. So, the total amount of money in Account A after 20 years is:
[tex]A=\$2800[/tex]
Since we initially deposited $2000 and our total is now $2800, this means that we earned an interest of [tex]2800-2000=\$ 800[/tex]
Account B:
Account B earns compound interest. Like Account A, Account B has a principal value of $2000 and the interest rate is 2% or 0.02. We also know that it's compounded annually, so once per year. We can use the compound interest formula:
[tex]B=P(1+\frac{r}{n}})^{nt}[/tex]
Where B is the future value, P is the principal, r is the rate, n is the times compounded per year, and t is the time in years.
So, let's substitute 2000 for P, 0.02 for r, n for 1 (since it's compounded annually), and t for 20. This yields:
[tex]B=2000(1+\frac{0.02}{1})^{(1)(20)}[/tex]
Simplify this to acquire:
[tex]B=2000(1.02)^{20}[/tex]
Evaluate. Use a calculator. So, after 20 years, the amount of money in Account B is:
[tex]B\approx\$2971.89[/tex]
Since our principal was $2000, this means that we earned an interest of approximately [tex]2971.89-2000=\$ 971.89[/tex].
So, Account A earned an interest of $800 and Account B earned an approximate interest of $971.89.
So, Account B earned more interest.
And it earned [tex]971.89-800=\$ 171.89[/tex] more than Account A.
And we're done!
