Question

A 5-year annuity of ten $4500 semiannual payments will begin 9 years from now, with the first payment coming 9.5 years from now. If the discount rate is 12% compounded monthly, what is the value of this annuity five years from now? What is the value three years from now? What is the current value of the annuity?

I have calculate the PVa at t=9 is 73073.68, but I don't know how to do the next steps...

Please explain as clearly as possible

Thanks!!

Answer 1

		Effective semi annual discount rate:
		Monthly discount rate =(12/12)%=	0.01
		Effective semi annual discount rate=R:
		1+R=(1+0.01)^6=	1.0615
		Effective semi annual discount rate=R:	0.0615	6.15%
		Present Value (PV) of Cash Flow:
		(Cash Flow)/((1+i)^N)
		i=Discount Rate=0.0615
		N=Period of Cash Flow
		Annuity Value 5 year from now
		N	A	B=A/(1.0615^N)
	Years from today	Semi annual Period from 5 years	Cash flow	Present value at period 0
	5	0	$0	$0
	5.5	1	$0	$0
	6	2	$0	$0
	6.5	3	$0	$0
	7	4	$0	$0
	7.5	5	$0	$0
	8	6	$0	$0
	8.5	7	$0	$0
	9	8	$0	$0
	9.5	9	$4,500	$2,629.86
	10	10	$4,500	$2,477.49
	10.5	11	$4,500	$2,333.96
	11	12	$4,500	$2,198.73
	11.5	13	$4,500	$2,071.35
	12	14	$4,500	$1,951.34
	12.5	15	$4,500	$1,838.28
	13	16	$4,500	$1,731.78
	13.5	17	$4,500	$1,631.45
	14	18	$4,500	$1,536.92
			SUM	$20,401.16
		Value of annuity five years from now	$20,401.16
		Number of periods from 3 years to 5 years	4	(2*2)
		Value of annuity Three years from now	$16,068.48	(20401.16/(1.0615^4)
		Number of periods from today to 3 years	6	(3*2)
		Current Value of annuity (Today)	$11,231.94	(16068.48/(1.0615^6)