Your client is 20 years old, and she wants to begin saving for retirem

QUESTION

Your client is 20 years old, and she wants to begin saving for retirement, with the first payment to come one year from now. She can save $11,000 per year, and you advise her to invest it in the stock market, which you expect to provide an average return of 11% in the future.If she expects to live f
a) If our client is 20 years old and she plans to retire at 65, then for 45 years she is depositing 11000 at the end of each year at an assumed 11% interest rate. In the financial calculator, we punch in the following: 45 [N] for the 45 years she deposits into her retirement account. 11 [I/Y] for the 11% interest rate. 0 [PV] since at present time (at age 20), there is no money in her account. 11000 [PMT] since she is depositing 11000 per period. [CPT] [FV] gives us the amount she will have in her account when she is 65, which is 10,853,024.15 (the calculator will show this as a negative amount because this is what can be withdrawn from the account, which is an outflow in relation to the account). Now, to find out how much she can withdraw at the end of each year for 20 years starting from age 65, we use the amount she will have at age 65 (10,853,021.15) as the PRESENT VALUE. The interest remains the same, the periods are set to 20, and the future value is set to 0 (since her account will have 0 when she finishes withdrawing her money at the end of 20 years). The key strokes are as follows: 20 [N] 11 [I/Y] 10,853,021.15 [PV] 0 [FV] [CPT] [PMT] = -1,362,875.42 (negative since this is what she WITHDRAWS from her account at the end of each year). b) For this part, we must start over to find out how much she will have saved by age 70. To do so, we set

the following: 50 [N] since she saves until age 70 (50 years of working) instead of 65 this time. 11 [I/Y] since interest has not changed in the second part of the question. 0 [PV] 11000 [PMT] [CPT] [FV] = a whopping 18,356,482.67 (again given as a negative). This number may seem high at first considering that there are just 5 more years of savings compared to retiring at 65, but consider that at 11% interest (a very high rate of return in the real world), simply holding 10 million dollars for 5 years gives us (1.11^5) X 10 million = 16.8506 million dollars. Now with 18,356,482.67, the amount she has saved up by age 70, we set this as the PRESENT VALUE, set the number of periods to 15, set the FUTURE VALUE to 0, and compute the payments. 15 [N] 11 [I/Y] 18,356,482.67 [PV] 0 [FV] [CPT] [PMT] = 2,552,748.66 (again, given as a negative since this is what she will withdraw at the end of each of 15 years).

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