Question

You have an uncle wants to see you be successful in life. He has no children of his own, so he’d like to do something for you, but at the same time instill a good work ethic.

He has promised to match up to 55% of what you make by working for your first 5 years of working. You have just graduated and found a job paying $45,000.

Your uncle was a financially savvy person. He understood that he could use a discount rate of 7.75% for the five years. What amount should the uncle set aside to fulfill his commitment to his nephew with the lowest cost to him?

Answer 1

Salary	$      45,000
Uncle promise	55%
Uncle promise	45000*55%
Uncle promise	$      24,750
PV of annuity
P = PMT x (((1-(1 + r) ^- n)) / r)
Where:
P = the present value of an annuity stream	P
PMT = the dollar amount of each annuity payment	$      24,750
r = the effective interest rate (also known as the discount rate)	7.75%
n = the number of periods in which payments will be made	5
PV of annuity=	PMT x (((1-(1 + r) ^- n)) / r)
PV of annuity=	24750*(((1-(1+7.75%) ^-5)) /7.75%)
PV of annuity=	$ 99,474.14
So Uncle should set aside this much money to fulfil his promise.