A nurse decides to save for her retirement at the age of 25 with the aim of retiring at 65. She plans for a retirement annuity of $1,000,000 at 65. She will make annual deposits, at the end of each year, and increase the payments by 10% every year after the initial deposit. Her Investment Advisor assures her that he can get her 7% compounded annually.What is the nurse's initial deposit for her retirement plan? Thanks for help.
There are a number of ways of solving this problem, using TVM formulas.However, there is a special formula that is rarely used and which was derived for this type of financial problems. It goes something like this:
Payment x [(rate of monthly increase^40 - interest rate^40) / (rate of increase - interest rate)]=1,000,000.
P*[(1.1^40 - 1.07^40) / (.10 - .07)]=1,000,000, solve for P
P=$990.60 The nurse's initial deposit.
