Math Skill 6 - Retirement TVM Calculations

Retirement problems are just TVM problems, like those in Math Skill 1 - they have an interest rate and payments over time. This means that you already know how to do these problems from skill 1, you just need to get used to the way these problems are worded.

The trick here is that these problems can sound much more complicated than regular TVM calculations because of every cashflow in the retirement scenario is in the future! The most important tip to keep in mind is that PV is not the value today – it is the value you have at the start of the time period in question. Similarly, the FV is not the value in the future. In most of these problems, everything is happening in the future! Focus on our original definition of FV – the value as the end of the time period.

Lastly, remember that the sign (positive of negative) on PV, FV, and PMT is based on whether the money is flowing to your wallet (so you can spend it), or away from your wallet (so you can’t spend it).

The solutions to these practice problems explain the logic of the question and how to think about these problems so that they are as easy to solve as any other TVM calculation.

Watch it in Action!

Practice Problems

1. Candice would like to retire in about 10 years but doesn’t know how much money she will need. She sits down and runs he numbers and decides that she would like to spend $40,000 per year after she is retired. If her investments earn an average of 4.2% for the entire 35 years she expects to be retired, how much will she need to have saved in order to retire?

2. Joe saves $5,000 per year in his IRA. Milly also saves $5,000 per year, but she uses her employer sponsored 401(k) plan with a 50% match. If they both earn 10% per year on average, how much money will they each have saved for retirement if they both save for 20 years?

3. Mike just retired with $1,000,000 in savings. He would like to be able to make this money last for 35 years. If his investments are expected to earn 7% per year, how much can he withdraw each month in order to meet this goal?

4. Beatrice wants to spend $50,000 per year in retirement. If she can collect $30,000 per year in Social Security benefits, her investments can earn 4%, and she expects to be retired for 25 years, how much money must she have saved in order to retire?

5. Monica just retired at age 67. She has $1,500,000 saved for retirement. She wants to live it up, so she withdraws $120,000 per year to live off. If her account earns 6% per year on average, how old will she be when she runs out of money?

6. Tyree has just retired with $2,200,000 in his 401(k). He wants to spend $90,000 per year in retirement, and his Social Security benefit is $32,000 per year. If his investments can earn 2.4% per year, how many years will it be before he runs out of money?

Solutions

1. What Candice really wants to know is how much she will have to have at the start of her retirement in order to run out after 35 years. When you think of it this way, the TVM components start to become clearer. We need to solve for PV – the amount at the start of the retirement period. Just because the start of retirement is in the future does not make it a future value. It’s a PV because it’s the start of the period of time over which she will withdraw her money. FV will be zero because she is running out of money at the end of her life. PMT will be positive because she is putting that money out of her account and into her wallet. This is a positive cash flow for your calculator.

FV = 0

PMT = 40,000 / 12 = $3,333.33 per month

I/Y = 4.2%

N = 35 * 12 = 420 months

Compute: PV = $732,841

2. Joe will save $5,000 per year, but Milly will save $5,000 plus her 0.50 * $5,000 = $2,500 per year from her employer match.

Joe:

PV = 0

PMT = -5,000 / 12 = $416.67 per month

N = 20 * 12 = 240 months

I/Y = 10 %

Compute: FV = $316,389

Milly:

PV = 0

PMT = -7,500 / 12 = -625 per month

N = 20 *12 = 240 months

I/Y = 10 %

Compute: FV = $474,580

3. What Mike really wants to know is if he starts his retirement with $1,000,000, how much can he withdraw each year in order to not run out of money before he dies. When you think about the problem this way, the pieces of the calculation make more sense.

PV = -1,000,000

N = 35 * 12 = 420 months

I/Y = 7 %

FV = 0

Compute: PMT = $6,388 per month

4. Like #1 and #3, the key to understanding this problem is to look at it from this perspective: How much does she have at the start of her retirement in order to run out of money exactly 25 years after retiring?

PMT = 20,000 / 12 = $1,666.67 per month (She needs $50,000 per year to maintain her lifestyle, but social security will give her $30,000 per year, so she only needs to withdraw $20,000 per year, or $1,666 per month from her account)

N = 25 * 12 = 300 months

I/Y = 4 %

FV = 0

Compute: PV = $315,754

5. She will run out of money about 23 years after she retires. Since she retired at age 67, she will run out of money at age 67 + 23 = 90 years old.

PV = -1,500,000

PMT = 120,000 / 12 = $10,000 per month

I/Y = 6 %

FV = 0

Compute: N = 277.9514 months / 12 = 23.16 years

6. This problem is just like #4, except we are solving for N instead of PV.

PV = -2,200,000

FV = 0

PMT = 90,000 – 32,000 = 58,000 per year / 12 = $4,833.33 per month

I/Y = 2.4 %

Compute: N = 1207.1 months / 12 = 100.59 years