Question

You win a judgment in an auto accident case for $102,500. You immediately receive $25,000 but must pay your lawyer's fee of $20,000. In addition, you will receive $2,500 a year for 25 years for a total of $62,500, after which the balance owed ($15,000) will be paid. If the interest rate is 7 percent, what is the current value of your settlement? Use Appendix B and Appendix D to answer the question. Round your answer to the nearest dollar.

Answer 1

PV of annuity for making payment
P = PMT x (((1-(1 + r) ^- n)) / r)
Where:
P = the present value of an annuity stream	To be computed
PMT = the dollar amount of each annuity payment	$          2,500
r = the effective interest rate (also known as the discount rate)	7.00%
n = the number of periods in which payments will be made	25
PV of annual payments=	PMT x (((1-(1 + r) ^- n)) / r)
PV of annual payments=	2500* (((1-(1 + 7%) ^- 25)) / 7%)
PV of annual payments=	$        29,134
PV of lump sum payment at t25 of $ 15000	Amount/(1+Interest)^time
PV of lump sum payment at t25 of $ 15000	15000/(1+7%)^25
PV of lump sum payment at t25 of $ 15000	$          2,764
Total PV of compensation:
PV of payment received today=	$        25,000
PV of annual payment received from t1 to t25=	$        29,134
PV of payment received at t25=	$          2,764
Total PV of compensation=	$        56,898
Less Lawyer's fee	$      (20,000)
Net compensation received	$        36,898