You are offered a contract with a signing bonus. If they offered you either $215,000 in cash or $2,000 a month for 15 years, guaranteed, which do you take (based strictly on the math)? Your safe rate of return is 7.5%.

Answer: Take the $2,000 monthly installments

Solution:

PV of an annuity = C*(1-(1+i/n)^(-n*t))/(i/n) = 2000*(1-(1+.075/12)^(-15*12))/(.075/12)

= 2000*(1-1.00625^-180)/.00625 = $215,746.85 (this is larger than $215,000...so take this)

C = Cash flow per period i = interest rate n = number of payments per year

t = number of years

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