Question

A debtor owing payments of $750 due today, $1,000 due in 2 years, and $1,250 due in 4 years requests a payout figure to settle all three obligations by means of a single economically equivalent payment 18 months from now. What is that amount, if the payee can earn 9.5% compounded semiannually? (Do not round your intermediate calculations and round your final answer to the nearest cent.)

Answer 1

Answer :

Amount owing today = $750

Amount due in 2 years = $1000

Amoun due in 4 years = $1250

Interest rate = 9.5% semi annually

Single economically equivalent payment is to be received by payee in 18 months from now.

Opportunity income lost on money which was to be received today will be received in 18 months

= [Amount(1+periodic interest)^{No of times compounding}] - Amount

Periodic interest = 0.095/2 = 0.0475

No of times compounding = 3(1.5 years of 6 months)

= [750(1+0.0475)³] - 750

= $112.03

Opportunity income gain on money which was to be received in 2 years will be received in 18 months

= [ Amount(1+periodic interest)^{No of times compounding}] - Amount

Periodic interest = 0.095/2 = 0.0475

No of times compounding = 1 (24 months - 18 months = 6 months interest earned, so 1 time compounding)

= [1000(1+0.0475)¹ - 1000

= $47.5

Opportunity income gain on money which was to be received in 4 years will be received in 18 moths

= [Amount(1+periodic interest)^{No of times compounding}] - Amount

Periodic interest = 0.095/2 = 0.0475

No of times compounding = 5 (48 months -18 months = 30 months interest earned. So 5 times of 6 months compounding period

= [1250(1+0.0475)⁵] - 1250

= $326.45

The amount payee earned = Opportunity income gain - Opportunity income lost

= ($326.45 + $47.5) - $112.03

= $261.92