Question

You have just turned thirty now and making a salary of $60,000 and you are determined to save for retirement. You have decided that you will save 10% of the salary each year into a

retirement fund that is expected to yield 9% per year. Your first contribution will be $6,000 (10% of the current salary) at the year-end (at your 31st birthday). If you expect your salary

to grow at 4% per year until retirement and expect to make the final contribution at age 69, what will be the balance of your fund at retirement? Also identify the type of cash flows

involved.

Answer 1

1)	The FV of a growing annuity is given by the formula:
	FVga = P*[(1+r)^n-(1+g)^n]/(r-g)
	Where
	P = the first payment
	g = growth rate
	r = interest rate
	n = number of periods
	Substituting values we have
	FVga = 6000*(1.09^39-1.04^39)/(0.09-0.04) =	$   29,03,954
2)	The type of cash flows involved is a GROWING ANNUITY.
	NOTE:
	The year of retirement is not given. Only the last payment
	year is given on the 69th birthday, which makes for 39
	payments.