Question

Gamorra loaned $9677.42 to Nebula. Nebula will pay Gamorra $10000 in 8 months. It’s now 3 months before the note will mature (when Nebula will pay off the note), but Gamorra can’t wait to get paid by Nebula. So, Gamorra contacted the manager at the Bank of Xander. The bank has agreed to buy the note from Gamorra at a discounted rate of 6%.

How much does Gamorra receive from the bank?

Answer 1

Formula for simple interest can be used to compute present value of notes at discount rate of 6 %.

A = P (1+rt)

A = Total accrued amount or Future value of note = $ 10,000

P = Principal amount or the amount to be paid now for the note

r = Discount rate = 6 % or 0.06 p.a.

t = Time period involved = 3 months or 3/12 = 0.25 years

Substituting all the values on above formula, we get P as:

$ 10,000 = P (1+ 0.06 x 0.25)

                 = P x (1+ 0.015)

                  = P x 1.015

P = $ 10,000/1.015 = $ 9,852.21674876847 or $ 9,852.22

Gamorra receives $ 9,852.22 from the bank now.