Question

9.A 10%,100-day note was dated 20 september 1992.the maturity value of the note was $3083.33.If the note was discounted on 17 november 1992 at 12%,FIND

i) the maturity date of the note
= 29 december 1992

ii)the face value of the note

$3083.33 = (1+0.1(100/360)
= 1.0278
= 3083.33/1.0278
= 2.999.9

or

= (1-0.1(100/360)
= 0.9722
= 3083.33/0.9722
= 3171.49

but the answer is = 5100

actually i still confuse what actually formula to find face value.we need - or + ?

Answer 1

I don't know how they came up with $5100; perhaps you should double check
that number.

In a discounted loan, the discounted
amount(Int.) is paid up-front by deducting it from the amount borrowed:

Ab = $2,000 = Amount borrowed = Face
value.
Ar = Amount received by borrower.
Ad = Amount discounted(Int.).
Rate = 10%
T = 180 Days.

Ar = Ab - Ad
Ar = Ab - Ab*r*T
Ar = 2000 - 2000*(0.1/360)*180
Ar = 2000 - 100 = $1900.

On the maturity date, borrower will pay
the face value (Ab) of $2000.

For a regular loan, the interest and
amount borrowed are paid on the maturity
date:

A = Ab + I
A = Ab + Ab*r*T
A = 2000 + 2000*(0.1/360)*180
A = 2000 + 100 = $2100 = Amt. paid on
the maturity date. On the date of the
loan, the borrower received $2,000.

NOTE: In both cases, the cost of the loan was $100.