You and your twin brother are considering investing towards your respective retirements (you have just celebrated your 22nd birthday, and plan on retiring at age 65). You will invest $2,500 per year into an account for each of the next 10 years (you will make the first payment immediately). After your 10th payment, you will not make any more payments, but will leave the accumulated funds in the account until you retire at age 65. Your brother, on the other hand, will wait exactly 10 years to make his first payment, but will then invest $2,500 each year for the next 33 years. Assuming a 12% annual rate of return on all investments, how much more will you have at age 65 than your brother?
Please show all work,