Question

The maturity value of a seven-month promissory note issued July 31, 2017, is $3275. What is the present value of the noto of the date of issue if interest is 7.75%?

Answer 1

The present value of a promissory note with a maturity value of $3275 due in seven months, issued with an interest rate of 7.75%, is calculated using the simple interest formula. The total interest over seven months at a monthly rate of 0.6458333% is $148.09. Subtracting the interest from the maturity value, the present value of the note is $3126.91.

Step-by-step explanation:

The student has asked to calculate the present value of a promissory note with a maturity value of $3275 that was issued on July 31, 2017, and is due in seven months with an interest rate of 7.75%. To determine the present value, we need to discount the future value of the note to today's dollars using the given interest rate.

First, we need to calculate the interest that accumulates over seven months on the note. Since the note's term is less than a year, we'll use simple interest:

1. Convert the annual interest rate to a monthly rate by dividing by 12: 7.75% / 12 = 0.6458333% per month.

1. Multiply the monthly interest rate by 7 (months) to get the total interest rate for the bond's term: 0.6458333% * 7 = 4.5208331% for seven months.

1. Determine the total interest by multiplying the total interest rate by the maturity value: 4.5208331% * $3275 = $148.09.

1. Calculate the present value by subtracting the total interest from the maturity value: $3275 - $148.09 = $3126.91.
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The present value of the note on the date of issue is $3126.91 assuming a simple interest method is appropriate, and interest is compounded monthly over the seven-month term.

However, this value may differ if the interest is compounded in a different manner (for example, daily or continuously), which would require a different calculation method.