Question

You are saving for retirement. To live​ comfortably, you decide you will need to save $ 4 million by the time you are 65. Today is your 35 th ​birthday, and you​ decide, starting today and continuing on every birthday up to and including your 65 th ​birthday, that you will put the same amount into a savings account. If the interest rate is 8 %​, how much must you set aside each year to make sure that you will have $ 4 million in the account on your 65 th ​birthday?

Answer 1

Number of deposits from 35th birthday till 65th birthday are = 31.

Interest rate = 8%

Required future value = $4,000,000.

Annuity annual payments are:

Payment required	=		FV*r /[(1+r)^n -1] * 1/(1+r)
Future value	FV		4,000,000.00
Rate per period	r
Annual interest			8%
Number of interest payments per year			1.00
Interest rate per period			0.08/1=
Interest rate per period			8.000%
Number of periods	n
Number of years			31.000
Payments per year			1
number of payments			31
Payment	=		4000000*0.08/ [(1+0.08)^31 -1] *1/(1+0.08)
	=		30,026.98

Payment required on each birthday is $30,026.98

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