Question

What is the value of an investment that is scheduled to pay you $10,000.00 in 6 years and that has an expected return of 8.22 percent, compounded semi-annually? (Round the value to 2 decimal places)

Answer 1

The present value of an investment that is expected to pay $10,000 in 6 years with an 8.22% return, compounded semi-annually, is approximately $6,157.97 when rounded to two decimal places.

Step-by-step explanation:

To determine the present value of an investment that is expected to pay a future amount, we use the formula for the present value (PV) of a future value (FV) in the context of compound interest:

PV = FV / (1 + r/n)nt

Where:

• FV is the future value of the investment, which is $10,000.00.
• r is the annual interest rate (as a decimal), so 8.22% becomes 0.0822.
• n is the number of times the interest is compounded per year, which is 2 for semi-annual compounding.
• t is the number of years until the payment is received, which is 6 in this case.

Now we can calculate the present value:

PV = $10,000.00 / (1 + 0.0822/2)2*6

Doing the math:

PV = $10,000.00 / (1 + 0.0411)12

PV = $10,000.00 / 1.041112

PV = $10,000.00 / (1.6239)

Using a calculator for the exponentiation:

PV = $10,000.00 / 1.6239

PV = $6,157.97

Therefore, the present value of an investment that will pay $10,000.00 in 6 years with an 8.22 percent return, compounded semi-annually, is approximately $6,157.97 (rounded to two decimal places).