You have your choice of two salary options:

$1.$ $$60,000$ a year paid in monthly installments $($paid at end of the month$)$

$2.$ $$48,000$ a year paid in monthly installments $($paid at end of the month$)+$ a signing bonus.

If you expect to stay at your job for three years, how much must the signing bonus be in order for you to be indifferent between the two options? Your required rate of return is $11\%.$