Question

# Derek decides that he needs \$117,748.00 per year in retirement to cover his living expenses. Therefore,...

Derek decides that he needs \$117,748.00 per year in retirement to cover his living expenses. Therefore, he wants to withdraw \$117748.0 on each birthday from his 66th to his 89.00th. How much will he need in his retirement account on his 65th birthday? Assume a interest rate of 9.00%

Derek plans to retire on his 65th birthday. However, he plans to work part-time until he turns 71.00. During these years of part-time work, he will neither make deposits to nor take withdrawals from his retirement account. Exactly one year after the day he turns 71.0 when he fully retires, he will wants to have \$3,117,388.00 in his retirement account. He he will make contributions to his retirement account from his 26th birthday to his 65th birthday. To reach his goal, what must the contributions be? Assume a 6.00% interest rate.

Amount required each year =\$117,748

Number of years = 24

Interest rate = 9%

Amount needed in account on 65th bday is equal to the present value of all future withdrawals

= 117,748*PVAF(9%,24years)

= 117,748*9.707

=\$1,142,979.84

Amount required in retirement fund on 72th bday = \$3,117,388

Amount required on 65th bday =3,117,388*PVF(6%, 7 years)

= 3,117,388*0.665

=\$2,073,063.02

Let annual contribution be X

X*[{(1.06)^40-1}/0.06] = 2,073,063.02

154.76x = 2,073,063.02

X = \$13,395.34

Hence, annual contribution required =\$13,395.34

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