Question

Your folks just called and would like some advice from you. An insurance agent just called them and offered them the opportunity to purchase an annuity for $23,634.31 that will py them $3,500 per year for 10 years. They don't have the slightest idea what return they would be making on their investment of $23,634.31. The rate of return would they be earning on their investment is what percent?

Answer 1

Calculation of rate of return
Particulars	Time	PVf @10%	Amount	PV
Cash Outflows	-	1.00	23,634.31	23,634.31
PV of Cash outflows = PVCO				23,634.31
Cash inflows	1.00	0.9091	3,500.00	3,181.82
Cash inflows	2.00	0.8264	3,500.00	2,892.56
Cash inflows	3.00	0.7513	3,500.00	2,629.60
Cash inflows	4.00	0.6830	3,500.00	2,390.55
Cash inflows	5.00	0.6209	3,500.00	2,173.22
Cash inflows	6.00	0.5645	3,500.00	1,975.66
Cash inflows	7.00	0.5132	3,500.00	1,796.05
Cash inflows	8.00	0.4665	3,500.00	1,632.78
Cash inflows	9.00	0.4241	3,500.00	1,484.34
Cash inflows	10.00	0.3855	3,500.00	1,349.40
PV of Cash Inflows =PVCI				21,505.98
NPV= PVCI - PVCO				-2,128.33
Statement showing NPV
Particulars	Time	PVf @5%	Amount	PV
Cash Outflows	-	1.00	23,634.31	23,634.31
PV of Cash outflows = PVCO				23,634.31
Cash inflows	1.00	0.9524	3,500.00	3,333.33
Cash inflows	2.00	0.9070	3,500.00	3,174.60
Cash inflows	3.00	0.8638	3,500.00	3,023.43
Cash inflows	4.00	0.8227	3,500.00	2,879.46
Cash inflows	5.00	0.7835	3,500.00	2,742.34
Cash inflows	6.00	0.7462	3,500.00	2,611.75
Cash inflows	7.00	0.7107	3,500.00	2,487.38
Cash inflows	8.00	0.6768	3,500.00	2,368.94
Cash inflows	9.00	0.6446	3,500.00	2,256.13
Cash inflows	10.00	0.6139	3,500.00	2,148.70
PV of Cash Inflows =PVCI				27,026.07
NPV= PVCI - PVCO				3,391.76
Internal rate of return=	Lower rate+	(Lower rate NPV)	*(Higher rate- lower rate)
		(lowe rate NPV- Higher rate NPV)
	5%+	3391.76	*(10%-5%)
		(3391.76+2128.33)
	5%+3.07%
Rate of return is 8.07%