Question

1. You deposit $12,000 annually into a life insurance fund for the next 30 year, after which time you plan to retire. (6 points in total)

1. If the deposits are made at the beginning of the year and earn an interest rate of 6.5 percent.  What will be the value of the retirement fund at the end of year 30?
2. Instead of a lump sum, you wish to receive annuities for the next 20 years (years 31 to 50).  What is the constant annual payment you expect to receive at the beginning of each year if you assume an interest rate of 6.5 percent during the distribution period?
3. Repeats (a) and (b) assuming an earning rate of 6.5 percent during the deposit period and an earning rate of 8 .5 percent during the distribution period.

Answer 1

a)	The beginning of the year deposits constitute an annuity due whose FV = 12000*1.065*(1.065^30-1)/0.065 =	$     11,03,870.76
b)	The above amount is the PV of the annuities (annuity due) to be received at the beginning or years 31 to 50.
	The annuity to be received = 1103870.76*(0.065*1.065^20)/((1.065^20-1)*1.065)) =	$           94,068.86
c)	The beginning of the year deposits constitute an annuity due whose FV = 12000*1.065*(1.065^30-1)/0.065 =	$     11,03,870.76
	The annuity to be received = 1103870.76*(0.085*1.085^20)/((1.085^20-1)*1.085)) =	$       1,07,508.85