Question

James Horner is considering an investment scheme, to fund his house purchase after 6 years, with following cash deposits for a period of 6 years.

Year	1	2	3	4	5	6
Cash deposit ($)	10,000	12,000	14,000	16,000	18,000	20,000

1. The rate of interest on the deposits is 9% per annum. If James requires an amount of $115,000 at the end of 6 years to purchase the property, how much will be the shortfall or surplus of this investment scheme? Show all the necessary calculations
2. If the rate of interest increases to 11%, what will be the surplus/shortfall
3. What will be your answer for a) above, If James deposits at the beginning of each year, instead of depositing at the end of the year?

Answer 1

	Ans a)
	Year	Cash deposit ($)	future value	Formula
	1	10000	15,386	=10000*(1+9%)^5
	2	12000	16,939	=12000*(1+9%)^4
	3	14000	18,130
	4	16000	19,010
	5	18000	19,620
	6	20000	20,000
	Future value		109,085
	therefore shortfall = 115,000-109085			5,915
	Ans b)
	Year	Cash deposit ($)	future value	Formula
	1	10000	16,851	=10000*(1+11%)^5
	2	12000	18,217	=12000*(1+11%)^4
	3	14000	19,147
	4	16000	19,714
	5	18000	19,980
	6	20000	20,000
	Future value		113,908
	therefore shortfall = 115,000-113908			1,092
	Ans C)
	Year	Cash deposit ($)	future value	Formula
	1	10000	16,771	=10000*(1+9%)^6
	2	12000	18,463	=12000*(1+9%)^5
	3	14000	19,762
	4	16000	20,720
	5	18000	21,386
	6	20000	21,800
	Future value		118,903
	therefore surplus =118903- 115,000			3,903