Question

You want to retire in 46 years with $10,000,000. You plan to start saving next year and then growing each retirement contribution by 1% per year. You are confident that you can compound your savings at 9% per year. How much must your first payment be?

(future value of growing annuity problem) - please show work

Answer 1

Using goal seek

first payment is 15656.72

	Future value of Growing annuity =	P/(r - g) × [ (1+r)n - (1+g)n]
P=	Periodic payment	15,656.72
g=	Growth rate	1%
r=	Rate of interest per period:
	Annual rate of interest	9.00000%
	Frequency of payment	once in every 12 months
	Payments per year	12/ 12=	1
	Interest rate per period	0.09/1=	9.00000%
n=	number of payments:
	Number of years	46
	Payments per year	1
	number of payments	46
	Future value of annuity=	15656.72/(0.09 - 0.01) × [ (1 + 0.09 )^46 - (1+ 0.01)^46 ]
	Future value of annuity=	10,000,002.45