Question

# Derek plans to retire on his 65th birthday. However, he plans to work part-time until he...

Derek plans to retire on his 65th birthday. However, he plans to work part-time until he turns 72.00. 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 72.0 when he fully retires, he will begin to make annual withdrawals of \$118,640.00 from his retirement account until he turns 89.00. After this final withdrawal, he wants \$1.26 million remaining in his 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 10.00% interest rate

First we will calculate present value of his 65th birthday

First present value at 72nd birthday

Annual withdrawal from 72 nd to 89 for 15 years at annual withdrawal of 118640

P.v = 118640(PVIFA 10% 15y)

= 118640(7.6061) = 902387

Now this is bought to present value at 65th year

=902388/(1.1)^7 = 463068

Lumpsum received on 89 birthday is 1260000

Pv as on 65 birthday is = 1260000/1.1^22 = 154785

Total present value at 65th birthday is 154785+ 463068 = 617853

Annual payment are done and their future Value should be 617853 for40 years

Let periodic payment is x

X(FVIFA 10% 40y) = 617853

X(442.59)= 617853

Periodic payment is 1395

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