Question

brandon wishes to accumulate 100,000 by making level monthly end of month deposits for 30 years into an account that earns 5.4% interest convertible monthly. after 10 years the interest rate increases to 6.6% convertible monthly. what should brandons new deposit amount be if he wishes to accumulate 100,000 at the end of 30 years?

Answer 1

Future value of annuity			=	P{(1+r)^n-1}/r
	here,
	Future value		=	$100,000
		rate	=	0.054/12=0.0045 per month
		time	=	30*12=360 months
		100,000	=	P[{(1+0.0045)^360}-1]/0.0045
		100,000	=	P*896.6133
		100,000/896.6133	=	P
		$111.53	=	P
	Monthly installment		=	$111.53
Future value of this investment after 10 years
		Rate	=	0.0045 per month
		time	=	10*12=120 months
	Future value after 10 years		=	111.53[{(1=0.0045)^120}-1/0.0045
			=	111.53*158.6509
			=	$17,694
	Value of $17694 after 20 years (i.e. 30 years from now @ 0.0055(0.066/12) per month)
			=	17694*(1+00.55)^240
	(this is value of single amount not annuity)		=	$65,997
	After 10 years additional amount (in future value terms)required
			=	100,000-65997
			=	$34,003
	Applying the formula of future value again
		34003	=	P[{(1+0.0055)^240}-1]/0.0055
		34003	=	P*545.9813
		34003/496.34	=	P
		$68.50	=	P
		New deposit is $68.5 per month
	There may be minor differences due to decimal places.