You are 30 years old today. You will start saving in 1 month. You will save every month up to (and including) your 60th birthday (360 saves). You will retire on your 60th birthday. You will earn 6% per annum (APR) on your savings and interest compounds monthly. You will commence withdrawing your retirement income 1 month after your 60th birthday. Your retirement withdrawal is $7,500 per month. You will make your last withdrawal on your 85th birthday (300 withdrawals) at which point your retirement account will be empty (no funds remaining). Your rate of return in retirement is only 4% per annum (APR), because you invest in less risky securities, and interest on your retirement savings compounds monthly.
(a) How much should you save each month for retirement?
(b) What is the effective annual rate (EAR) for the interest you earn on your retirement savings during the accumulation period (before your 60th birthday)?
(c) A friend aged 45 retirement savings’ interest compounds quarterly. What interest rate must the savings earn quarterly to have an equivalent EAR to your pre-retirement savings?
(d) What is the effective annual rate (EAR) for the interest you earn on your retirement savings during the decumulation period (after your 60th birthday)?
(e) A new retirement income product (used after age 60) with similar risk to your existing retirement income product offers a rate of 4.1% (APR) compounded quarterly. Is it a good financial decision to transfer your retirement funds from your existing retirement income product to the new retirement income product? Assume there are no transaction costs and justify your answer.