Question

Anne Katz, the owner of Katz Sport Shop, lends $8,000 to Shelley Slater to help her open an art shop. Shelley plans to repay Anne at the end of eight years with interest compounded semiannually at 8%. At the end of eight years, Anne will receive:

Answer 1

To find the amount Anne will receive, we use the future value formula for compound interest. After inserting the values and calculating, the future value comes out to be $14,937.43, which Anne will receive at the end of eight years.

Step-by-step explanation:

Calculating Compound Interest

The student is asking about the future value of an investment with compound interest. To calculate this, we use the formula FV = P(1 + r/n)nt, where FV is the future value, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years the money is invested. In this case:

Principal (P) = $8,000

Annual interest rate (r) = 8% or 0.08

Compounded semiannually means n = 2

Time (t) = 8 years

Inserting these values into the formula gives us:

FV = $8,000(1 + 0.08/2)2*8 = $8,000(1 + 0.04)16

Calculating the value inside the brackets first:

1 + 0.04 = 1.04

Now raise 1.04 to the 16th power and multiply by $8,000:

FV = $8,000 * 1.0416

After calculating this, we find that the future value FV that Anne will receive is:

FV = $14,937.43