Question

John is currently 25 years old. He has $10,000 saved up and wishes to deposit

this into a savings account which pays him J12 = 6% p.a. He also wishes to
deposit $X every month into that account so that when he retires at 55, he can
withdraw $2000 every month end to support his retirement. He expects to live up till 70 years. How much should he deposit every month into his account?
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Answer 1

$832.22

Explanation:

John wishes to withdraw $2000 every month when he retires at 55 till he's 70

So there are 70 - 55 = 15 years of withdrawing $2000 monthly.

Amount to be withdrawn in 15 years monthly = $2000*12*15= $360000

So he needs $360000to achieve this goal.

But he is currently 25 and has $10000.

55-25 = 30 years.

6% per annum

A = 10000(1+(0.06/30))^(30*30)

A= 10000(1+0.002)^(900)

A= 10000(1.002)^(900)

A= 10000(6.04)

A= 60400

His savings gave him $60400

But he needs $360000

He still needs

360000-60400= 299600

So how much will he deposit every month for 30 years to give 299600

30*12= 360

He will deposit 360 times.

Then 299600/360= $832.22

He will deposit$ 832.22 every month for 30 years.