Final answer:
To calculate the present value of the promissory note, use the formula for present value in simple interest and input the given values. After converting the time to years and the interest rate to a decimal, the calculation results in an approximate present value of $3883.50 for the note.
Step-by-step explanation:
The student has asked how to determine the present value of a promissory note with a maturity value of $4000, given a 9% simple interest rate for a term of 4 months.
To calculate this, we need to find out how much money should be invested now at a 9% annual interest rate to grow to $4000 in 4 months. The formula for the present value (PV) in the case of simple interest is given by PV = M / (1 + rt), where M is the maturity value, r is the annual interest rate as a decimal, and t is the time in years.
First, let's convert the interest rate and time to be compatible:
- Interest rate: 9% annual = 0.09
- Time: 4 months = 4/12 year = 1/3 year
We then plug these values into the formula:
PV = 4000 / (1 + 0.09 * (1/3))
PV = 4000 / (1 + 0.03)
PV = 4000 / 1.03
PV ≈ $3883.50
Thus, the present value of the promissory note is approximately $3883.50.