Payments of 75 each are made every 2 months from September 1, 2006 to July 1,...

Payments of 75 each are made every 2 months from September 1, 2006 to July 1, 2011, inclusive. For each of the following cases draw the time diagram line and find the value of the series:

(a) 2 months before the first payment at effective compound annual interest rate i = 0.05;

(b) 10 months before the first payment at nominal interest rate i(12) = 0.12 compounded monthly;

(c) 2 months after the final payment at nominal discount rate d(4) = 0.08 compounded quarterly;

(d) one year after the final payment at annual force of interest δ = 0.07.

Expert Solution

	(a) 2 months before the first payment at effective compound annual interest rate i = 0.05;

	Assume September 1,2006 as Month 0
	July 1, 2011, Month=58

	Effective annual rate=0.05
	Effective monthly rate=r
	(1+r)^12=1.05
	1+r=(1.05^(1/12))=	1.004074
	r=Effective monthly rate=	0.004074

	Present Value (PV) of Cash Flow:
	(Cash Flow)/((1+i)^N)
	i=Discount Rate=0.004074
	N=Month of Cash Flow		(a)	(b)	.(c)	(d)
	N	A	B=A/(1.004074^N)	C=A/(1.01^N)	D=A/(1.006623^N)	E=A/(1.005654^N)
Date	Month	Cashflow	PV of cash flow at 0.004074	PV of cash flow at 0.01	PV of cash flow at 0.006623	PV of cash flow at 0.005654
.Sep.1,2006	0	75	75	75	75	75
.Nov.1,2006	2	75	74.39261	73.5222	74.01633	74.15904
.Jan.1,2007	4	75	73.79015	72.07353	73.04557	73.32751
.Mar.1,2007	6	75	73.19256	70.65339	72.08753	72.5053
.May.1,2007	8	75	72.59981	69.26124	71.14207	71.69231
.July.1,2007	10	75	72.01186	67.89652	70.209	70.88844
.Sep.1,2007	12	75	71.42868	66.55869	69.28817	70.09358
.Nov.1,2007	14	75	70.85021	65.24722	68.37941	69.30763
.Jan.1,2008	16	75	70.27643	63.96159	67.48258	68.5305
.Mar.1,2008	18	75	69.7073	62.7013	66.59751	67.76208
.May.1,2008	20	75	69.14278	61.46584	65.72404	67.00228
.July.1,2008	22	75	68.58283	60.25472	64.86204	66.25099
.Sep.1,2008	24	75	68.02741	59.06746	64.01133	65.50813
.Nov.1,2008	26	75	67.47649	57.9036	63.17179	64.7736
.Jan.1,2009	28	75	66.93004	56.76267	62.34326	64.04731
.Mar.1,2009	30	75	66.38801	55.64422	61.52559	63.32916
.May1,2009	32	75	65.85036	54.54781	60.71865	62.61906
.July.1,2009	34	75	65.31708	53.473	59.92229	61.91692
.Sep.1,2009	36	75	64.78811	52.41937	59.13637	61.22266
.Nov.1,2009	38	75	64.26342	51.3865	58.36077	60.53618
.Jan.1,2010	40	75	63.74299	50.37399	57.59533	59.8574
.Mar.1,2010	42	75	63.22677	49.38142	56.83994	59.18623
.May.1,2010	44	75	62.71473	48.40841	56.09445	58.52259
.July.1,2010	46	75	62.20683	47.45457	55.35874	57.86638
.Sep.1,2010	48	75	61.70305	46.51953	54.63268	57.21754
.Nov.1,2010	50	75	61.20335	45.60291	53.91614	56.57597
.Jan.1,2011	52	75	60.7077	44.70435	53.209	55.94159
.Mar.1,2011	54	75	60.21606	43.8235	52.51113	55.31433
.May.1,2011	56	75	59.7284	42.96001	51.82242	54.6941
.July.1,2011	58	75	59.24469	42.11352	51.14274	54.08083
		SUM	2004.711	1711.143	1870.147	1919.73

	Value of the series on the date of first payment	2004.71
	Value of the series 2 months before the date of first payment	1988.48	(2004.71/(1.004074^2)


	(b) 10 months before the first payment at nominal interest rate i(12) = 0.12 compounded monthly;

	Monthly interest =(0.12/12)=	0.01

	Value of the series on the date of first payment	1711.14
	Value of the series ten months before the date of first payment	1549.08	(1711.14/(1.01^10)

	(c) 2 months after the final payment at nominal discount rate d(4) = 0.08 compounded quarterly

	Quarterly interest=(8/4)=2%=	0.02
	Effective annualinterest =(1.02^4)-1	0.082432
	Effective Monthly Interest =r
	(1+r)^12=1.082432
	1+r=(1.082432^(1/12)	1.006623
	Effective Monthly Interest =r=	0.006623

	Value of the series on the date of first payment	1870.15
	Value of the series 2 months after final payment ie(58+2)=60 months after first payment	2778.99	(1870.15*(1.006623^60)

	(d) one year after the final payment at annual force of interest δ = 0.07.

	Monthly effective interest=r
	(1+r)^12=1.07
	1+r=(1.07^(1/12)=	1.005654
	Monthly effective interest=r=	0.005654

	Value of the series on the date of first payment	1919.73
	Value of the series one year after final payment ie, (58+12)70months after first payment	2848.66	(1919.73*(1.005654^70)

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