brandon wishes to accumulate 100,000 by making level monthly end of month deposits for 30 years...

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brandon wishes to accumulate 100,000 by making level monthly end ofmonth deposits for 30 years into an account that earns 5.4%interest convertible monthly. after 10 years the interest rateincreases to 6.6% convertible monthly. what should brandons newdeposit amount be if he wishes to accumulate 100,000 at the end of30 years?

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4.3 Ratings (917 Votes)


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.

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brandon wishes to accumulate 100,000 by making level monthly end ofmonth deposits for 30 years into an account that earns 5.4%interest convertible monthly. after 10 years the interest rateincreases to 6.6% convertible monthly. what should brandons newdeposit amount be if he wishes to accumulate 100,000 at the end of30 years?

brandon wishes to accumulate 100,000 by making level monthly end of month deposits for 30 years...

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Finance

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