Your father is 50 years old and will retire in 10 years. He expects to live for

Question

Your father is 50 years old and will retire in 10 years. He expects to live for 25 years after he retires, until he is 85. He wants a fixed retirement income that has the same purchasing power at the time he retires as $55,000 has today. (The real value of his retirement income will decline annually after he retires.) His retirement income will begin the day he retires, 10 years from today; and he will then receive 24 additional annual payments. Annual inflation is expected to be 3%. He currently has $55,000 saved, and he expects to earn 9% annually on his savings. How much must he save during each of the next 10 years (end-of-year deposits) to meet his retirement goal?

Explanation / Answer

There were a couple typos in my original answer. See if this one clears things up.


The question asks us to determine how much he needs to save in each of the next 10 years (meaning we will eventually be computing a PAYMENT) to meet his retirement goal. However, we do not know what his retirement goal is, and must first figure that out.

He wants his annual income to have the same purchasing power as 55,000 today. This means that the value is multiplied by to get:
55000 X (1.03)^(10) = 73915.40

This is the amount your father receives the day he retires, 10 years from now. Note that his payments are at the beginning of each year from the day of his retirement. Because of this, we need to set the calculator to BGN if it is in END mode (most problems involve END payments so by default the calculator is usually set to END). On the BA-II+ the keystroke command is

[2nd] [PMT] (to get [BGN])
[2nd] [ENTER] (to get [SET])
and finally [2nd] [CPT] (to get [QUIT] to return to the main screen).

The tricky part of this question is that you need to factor inflation into the interest rate. Your father will want to receive payments that increase by 3% per year in order to balance out inflation and maintain his purchasing power.

He stands to earn 9% per year on his investment. If the money he receives annually is to increase by 3% per year, he will need to deposit more money initially. If we factor the inflation rate out of the interest rate, we can find out how much he needs in his retirement account initially.

1.09/1.03 = 1.05825

So 5.825% is the interest rate we will work with. Now we punch everything into our calculator.
25 [N] for the 25 years of payments your father wants
5.825 [I/Y] for the interest rate
73,915.4 [PMT] for the amount that he will receive (inflow) each year
0 [FV] for the 0 dollars left in his retirement account at the end of the the 25 years
[CPT] [PV] = -1,016,772.18

This is how much he must have in his account at the end of 10 years beginning today in order to meet his retirement goal.

Now, we use this value as our FUTURE VALUE to figure out how much he will need to deposit for 10 years. Because his deposits will occur at the end of the year, we need to change from BGN back to END. Simply enter the same keystroke commands as before to reverse it back to END mode.

Now we enter the following values:

-1,016,772.18 [FV]
10 [N]
9 [I/Y] We use the 9% interest rate because this is what he makes on his account. Inflation only factors in when dealing with retaining purchasing power. In this case, we do not factor inflation.
55,000 [PV] since he currently has 55,000 saved.

[CPT] [PMT] = 58,353.93 is how much he will need to save at the end of each of the next 10 years to reach his goal.

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