Question

You deposit $8000 in an account that pays 5% interest compounded quarterly.

A. Find the future value after one year.
B. Use the future value formula for simple interest to determine the effective annual yield.

Answer 1

The future value after one year is $8204.24. The effective annual yield is 5.095%.

Step-by-step explanation:

To find the future value after one year, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

• 
  
• A = future value
• 
  
• P = principal amount ($8000 in this case)
• 
  
• r = annual interest rate (5% as a decimal)
• 
  
• n = number of times interest is compounded per year (4 for quarterly)
• 
  
• t = number of years (1 in this case)

Plugging in the values, we get:

A = 8000(1 + 0.05/4)^(4*1) = $8204.24

As for the effective annual yield, since the interest is compounded quarterly, we'll use the formula:

Effective Annual Yield = (1 + r/n)^n - 1

Plugging in the values, we have:

Effective Annual Yield = (1 + 0.05/4)^4 - 1 = 5.095%