Retirement saving

Deryl wishes to save money to provide for his retirement. Beginning one year from now, he will begin depositing the same fixed amount each year for the next 30 years into a retirement savings account. Starting one year after making his last deposit, he will withdraw $100,000 annually for the following 25 years (i.e., he will make 25 withdrawals in all). Assume that the retirement fund earns 12% annually over the period he is depositing money and the period he makes withdrawals. For Deryl to have sufficient funds in his account to fund his retirement, how much should he deposit annually (rounded to the nearest dollar)?

Correct answer:

x =  3640 USD

Step-by-step explanation:

q=100%+12%=1+10012=1.12 n=30 m=25 w=100000 USD/a  k1=q1qn1=252812528n1=1.1211.12301241.3327  k2=q1qm1=252812528m1=1.1211.12251133.3339  k3=qm1=1.1225115.1786  x k1 qm1=w k2  x=k1 k3k2 w=241.3327 15.1786133.3339 1000003639.9197 USD   Verifying Solution:  s1=x k1=3639.9197 241.3327878431.5806 USD  (((((((((((((((((((((((((X k1w) qw) qw) qw) qw) qw) qw) qw) qw) qw) qw) qw) qw) qw) qw) qw) qw) qw) qw) qw) qw) qw) qw) qw) qw) q=0 (((((((((((((((((((((((((X 241.33268434093100000) 1.12100000) 1.12100000) 1.12100000) 1.12100000) 1.12100000) 1.12100000) 1.12100000) 1.12100000) 1.12100000) 1.12100000) 1.12100000) 1.12100000) 1.12100000) 1.12100000) 1.12100000) 1.12100000) 1.12100000) 1.12100000) 1.12100000) 1.12100000) 1.12100000) 1.12100000) 1.12100000) 1.12100000) 1.12=0  4102.671177X=14933393.4462  X=4102.6711772314933393.4462=3639.91965262  X=3639.919653

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Math student
Inflation destroy this scheme

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