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 25 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 3 %, 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?

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Dryomys Dryomys · Answer 1 · 2019-10-04T08:06:47+02:00

Answer: $50,846.3701

Explanation:

Need to save $4 million to live comfortably,

Interest rate, r = 3%

N = 40 years

[tex]Present\ value=\frac{FV_{N} }{(1+i)^{N}}[/tex]

[tex]Present\ value=\frac{4,000,000 }{(1+0.03)^{40}}[/tex]

[tex]Present\ value=\frac{4,000,000 }{3.262}[/tex]

= 1,226,241.57

[tex]Present\ value\ of\ annuity= C\times\frac{1}{i}\times(1-\frac{1}{(1+i)^{N}}) + C[/tex]

[tex]1,226,241.57= C\times\frac{1}{0.03}\times(1-\frac{1}{(1.03)^{40}})+C[/tex]

[tex]1,226,241.57=C[\frac{1}{0.03}\times(1-0.3065)+1][/tex]

[tex]1,226,241.57=24.1166\times C[/tex]

[tex]C=\frac{1,226,241.57}{24.1166}[/tex]

= $50,846.3701

Hence, $50,846.3701 will be the annual payment to have $4 million in the account on 65th birthday.