Question

You need $25,000 in today's buying power, 5 years from now. You can earn 2% APR in real terms on your investments. How much must you invest (a different amount each year), starting next year for 4 years to just meet your needs, if you expect inflation to be 4% per year? The amount you invest should just maintain the real cash values.

Answer 1

Formula sheet

A	B	C	D	E	F	G	H	I
2
3		Future Value	25000	(Todays Buyinh power i.e. in real terms)
4
5		Period (n)	5	years
6		Real Interest Rate	0.02	per Year
7		Inflation Rate	0.04
8		Nominal Value required at 5th year	=D3*(1+D7)^D5	=D3*(1+D7)^D5
9
10		Assuming that amount deposited is X per year for 4 years.
11		Nominal amount is discounted at nominal rate.
12
13		Nominal interest rate	=[(1+Real interest rate)*(1+inflation Rate)]-1
14			=((1+D6)*(1+D7))-1	=((1+D6)*(1+D7))-1
15
16		Future value of first 4 years annuity at year 5	=X*(F/A,6.08%,4)*(F/P,6.08%,1)
17
18		(F/A,6.08%,4)	=FV(D14,4,-1,0)	=FV(D14,4,-1,0)
19		(F/P,6.08%,1)	=(1+D14)^1	=(1+D14)^1
20
21		Future value of first 4 years annuity at year 5	=X*(F/A,6.08%,4)*(F/P,6.08%,1)
22			=X*4.38*1.0608
23			=X*4.646
24		Future value of annuity at Year 5 should be equal to the future value required i.e.
25		X*4.646 =$30,416.32
26
27		Solving the above equation X can be found as below:
28		X=	=D8/(D18*D19)	=D8/(D18*D19)
29
30		Hence the annual amount to be deposited for 4 years is	=D28
31