Question

You want to have $300,000 in real terms 7 years from now.
You expect inflation over that time period to be 4% per year. Your investments earn 7% APR (nominal) compounded annually.
Based on your expectations, you construct a growing nominal annuity to meet your investment target. What is the nominal cash-flow you would have to deposit in year 5 if inflation turns out to what you expected?

Answer 1

The growing annuity would be
FV[GA] = P*[((1+r)^n-(1+g)^n))/(r-g)
where
P = The first payment
r = rate per periiod
g = growth rate (here inflation)
n = number of periods
The amount required in nominal terms = 300000*1.04^7 =		$      394,780
Substituting values we have
394780 = P*[1.07^7-1.04^7)/(0.07-0.04)]
Solving for P
P = 394780/((1.07^7-1.04^7)/0.03))	$   40,860.49
So the first payment = $40860.49
The fifth payment would be 40860.49*1.04^4 =		$ 47,800.99
Check:
Year	Payment with 4% increase every year	FVIF at 7%	FV
1	40860.49	1.50073	61321
2	42494.91	1.40255	59601
3	44194.71	1.31080	57930
4	45962.49	1.22504	56306
5	47800.99	1.14490	54727
6	49713.03	1.07000	53193
7	51701.56	1.00000	51702
	Total amount		394780