Question

An 11-year $8000.00 promissory note, with interest at 8.4% compounded monthly, is discounted at 6.5% compounded semi-annually yielding proceeds of $14 631.15. The note was discounted _____ months before the due date.

Answer 1

Future value = present value * (1 + r)ⁿ,

where r = interest rate per period

n = number of periods

Future value of note after 11 years = $8000 * (1 + (8.4%/12))^11*12

Future value of note after 11 years = $20,090.11

Present value = future value / (1 + r)ⁿ

Let us say the note is discounted X semiannual periods before it is due. Then :

$14 631.15 =  $20,090.11 / (1 + (6.5% / 2))^X

1.0325^X = ($20,090.11 / $14 631.15)

X = log_1.0325($20,090.11 / $14 631.15)

X = 9.914

The note is discounted 9.914 semiannual periods before it is due.

Number of months = 9.914 * 6 = 59.48

The note is discounted 59.48 months before it is due.