Videos: Back-to-Back Annuities
Deferred Annuities
1. You plan to retire in 21 years. You will need 25 annual payments of $30,000 with the first payment to be received in 21 years. Interest is calculated at 10% effective.
(a) How much money should you set aside today for your retirement?
Back-to-Back Annuities
(b) Instead of making one large payment you would like to make 21 annual payments starting today. Find the size of these payments.
(c) How much of your retirement annuity in part (b) is interest?
(d) Re-answer b, assuming you make the payments starting in one year.
(e) How much of your retirement annuity in part (d) is interest?
2. You are saving money for your retirement. Starting in six months and for five years you invest $1,500 every 6 months in a mutual fund that pays 6% compounded semi-annually. After five years, the rate drops to 4.8% compounded quarterly and you decide to deposit $1,000 every quarter for another five years. How much money will you have at the end of ten years?
3. You would like to save enough to take a 2 year sabbatical in 15 years. Starting today, you make your first of 180 monthly deposits of $500 into an account that pays j12=9%.
(a) One month after making your last deposit you take your first of 24 monthly payments. Find the size of these payments.
(b) Two months after making your last deposit you take your first of 24 monthly payments. Find the size of these payments.
Summary of Back to Back Annuities
Chapter Attribution
Video chapter in Business Mathematics by Chris Kellman, Leslie Major, Don Mallory, Frank Gruen, and Amy Goldlist shared under a CC BY-NC license.
