Question

Two annuities are available for purchase that your client has identified. The first annuity pays $7,000 each six-month period over a 5 year period, at a nominal rate of 9% p.a. The annuity has an annual fee of $300, paid at the beginning of each year. The second annuity pays $1,000 each month, again over 5 years at a nominal rate of 10% p.a.and does not have an annual fee.If each of the annuities cost $50,000, identify which of the annuities you would recommend to your client.

Answer 1

1st annuity 2nd annuity 2 payment per 6-month period 3 payment permonth 4 annual fee 5 period 6 cost of annui 7 nominal rate 8 rate per 6-month 9 rate per month 1000 0 0.09 0.045 0.00833333 12 Present value of annual fee 1271.92 55389.03 13 present value of annuit 15 effective present value of ann 16 net present value of annuit 54117.1147065.37 4117.11 -2934.63 18 I would recommend the first annuity to my client since the net present value of annuity for 1st annuity is 19 sitive and the 2nd annuity gives a negative value

1st annui 2nd annui 2 payment per 6-month period 3 payment permonth 4 annual fee 5 period 6 cost of annui 7 nominal rate 8 rate per 6-month 9 rate per month 7000 1000 300 0 50000 50000 0.09 B7/2 C7/12 12 Present value of annual fee -PV(B7,B5,B4,,1 -PV(B8,B5*2,B2,,0) 13 present value of annuit 15 effective present value of annuity 16 net present value of annuit 17 B13-B12 B15-B6 -PV(C9,C5 *12,C3,,0) -C15-C6