Question

A debt of $3726.12 is due August 1, 2022. What is the value of the obligation on February 1,2015 , if money is worth 9% compounded monthly? The value of the obligation is $ (Round to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Answer 1

The present value of a $3726.12 debt due on August 1, 2022, with a 9% annual interest rate compounded monthly, as of February 1, 2015, is calculated using the present value formula for a single sum.

Step-by-step explanation:

To calculate the present value of a debt of $3726.12 due on August 1, 2022, when money is worth 9% compounded monthly, you use the formula for present value of a single sum:

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

Where:

• PV = Present Value
• FV = Future Value ($3726.12)
• r = annual interest rate (0.09)
• n = number of times the interest is compounded per year (12)
• t = time in years from the present until the debt is paid

Given that the debt is due on August 1, 2022, and we want the value on February 1, 2015, t = 7 years and 6 months = 7.5 years.

So the calculation with the given numbers:

PV = $3726.12 / (1 + 0.09/12)(12*7.5)

Using this formula, we can calculate the present value of the obligation.