Derek and Becky are a married couple with three children.

Becky does not currently work, and she does not expect to return to work for at least $6$ years, at which time she believes that her take$-$home pay would be about $$4,500$ per month. However, Derek would feel better if he knew that she could manage the household financially without working until their son turns $18.$ Neither of them currently earns investment or pension income.

If Derek dies, Becky would be eligible for a Canada Pension Plan $($CPP$)$ survivor benefit of about $$570$ per month, and all three of the children would be eligible for a CPP benefit of about $$230$ per month as children of a deceased CPP contributor.

Derek wants to ignore any potential benefits his family could receive under his province's Workers' Compensation Board, because there is no guarantee that his death will be work$-$related.

Derek's non$-$registered investment portfolio currently produces after$-$tax income of $$7,200$ annually, but because these assets may be needed to meet estate expenses, this income is not being included at this point.

If Derek were to die Beckey would have a monthly income of $$1,260($CPP would provide $$570$ for Becky and $$230$ for each child$)$ and monthly expenses of $$4,150.$ If the after tax inflation adjusted rate of return is $1\mathrm{.}71\%$ what is the capitalized income shortfall? In other words, how much insurance does Derek need to make up for this income shortfall?