Question

Determine the present value, discounted at 6 percent per year, of $50,000 to be received five years from today if the interest rate is compounded semiannually and quarterly?

Answer 1

To determine the present value of $50,000 received five years from today, we need to calculate the present discounted value using the given interest rate and compounding frequency. For semiannual compounding, the present value is X, and for quarterly compounding, the present value is Y.

Step-by-step explanation:

To determine the present value of $50,000 to be received five years from today, we need to calculate the present discounted value using the given interest rate and compounding frequency.

1. For semiannual compounding: The interest rate is 6% per year and compounded semiannually, so the effective interest rate per compounding period is 6% / 2 = 3%.

2. For quarterly compounding: The interest rate is 6% per year and compounded quarterly, so the effective interest rate per compounding period is 6% / 4 = 1.5%.

Now we can calculate the present value using the present value formula:

Present Value = Future Value / (1 + r)n

Where:

• Future Value: $50,000
• r: Effective interest rate per compounding period (3% for semiannual compounding, 1.5% for quarterly compounding)
• n: Number of compounding periods (5 years for both cases)

Using the formula, calculate the present values for both compounding frequencies separately.