The best way to do this is to draw a picture of ΔFKL and include line segment KM that is perpendicular to FL. This creates ΔFKM which is a 45°-45°-90° triangle and ΔLKM which is a 30°-60°-90° triangle.
Find the lengths of FM and ML. Then, FM + ML = FL
<u>FM</u>
ΔFKM (45°-45°-90°): FK is the hypotenuse so FM =
<u>ML</u>
ΔLKM (30°-60°-90°): from ΔFKM, we know that KM = , so KL =
<u>FM + ML = FL</u>
=
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:
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:
Multiply and add:
Multiply. So, the total amount of money in Account A after 20 years is:
Since we initially deposited $2000 and our total is now $2800, this means that we earned an interest of
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:
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:
Simplify this to acquire:
Evaluate. Use a calculator. So, after 20 years, the amount of money in Account B is:
Since our principal was $2000, this means that we earned an interest of approximately .
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 more than Account A.
And we're done!