Two annuities, which your client has identified, are available for purchase. The first annuity pays $$6,000$ each three$-$month period over $4$ years, at a nominal rate of $12\%$ p$.$a$.$ This annuity also has a lump sum payment at maturity $($at the end of the $4$th year$)$ of $$30,000.$

The second annuity pays $$2,500$ each month, again over $4$ years, at a nominal rate of $11\%$ p$.$a$.$ This investment has an annual fee of $$1,000,$ paid at the start of the year, starting immediately.

If each of the annuities cost $$100,000,$ identify which $($if any$)$ of the annuities you would recommend to your client.