I ended my last article with a question, * how long does it take to save $50,000 for a down payment if you save $20 per day and earn 5% per annum on your portfolio*?

Remember to change the assumptions and work the answer out by yourself. I have a suggestion at the end if you’re interested in homework.

To ballpark the answer, you could divide the target ($50,000) by the savings rate ($20 per day) and get 2,500 days (50,000 / 20) or about seven years (2,500 / 365 = 6.8).

Throughout this entire series remember that ** small daily changes can have large long-term effects**.

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The value of a series of cash flows is tough to calculate by hand but financial calculators and spreadsheets have formulas to help us out. Let’s work through this example:

- Payment is $20 per day
- i = 5% per annum

We have a mismatch between the period of the savings (daily) and the return on investment (annual). We need the payment period (daily) to match the investment return period (annual).

The easy way to convert is to divide the annual rate by 365 days to get a daily rate. 5.0% / 365 = 0.014%

You could go the other way and say that you were saving $7,300 per annum ($20 per day times 365 days) but all of us do better with smaller, frequent targets. $20 day sounds a lot more reasonable than $7,300 per annum – but they are the same!

**Side-note**: Your finance professor would tell you that, strictly speaking, to get the exact rate you’d need to use the formula *[(1+i)^(1/365)] – 1*. That equals 0.013% and reflects the compounding effect of interest on your interest across the year. My advice would be keep it simple and divide the annual rate by 365 to get your daily rate. It will be close enough.

Your future target is $50,000 and is called the future value (FV).

You want to calculate how long it will take to get the future value if you save $20 daily. Put differently, how many periods of saving are required to achieve my future value (FV) if I make a payment (PMT) of $20 per period and earn 0.014% per period (i)?

Now we have all the info…

- PV = $0
- FV = $50,000
- PMT = -$20 (notice the negative sign, you are paying out)
- i = 0.014%

The formula in google docs is =nper(rate,PMT,PV,FV) // and kicks out an answer of 2,150 days. It is easy to be intimidated by these formulas but most software packages have pop-up menus that help you along (nper = tell me the number of periods).

Our original estimate of 2,500 days wasn’t far off but that little bit of interest (0.014% per day) got us to the down payment one year quicker.

Both the $20 and the 0.014% are an example of how little things can make a big difference over time.

With mortgage rates at a 40-year low, a $50,000 down payment is very useful. In Boulder, it’s now cheaper to own, than to rent – providing you have the down payment and qualify for a low-rate mortgage.

**Saving small and frequently creates capital for investment.**

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*If you’re interested in homework then how long will it take to achieve a $75,000 portfolio if I can save $1,000 per month and earn 7.5% per annum on my savings. Bonus points – if your marginal tax rate is 27.5% then how much longer do you have to save to achieve your goal?*

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**Side-note**: when I learned all this stuff in the 80s, everybody used 10% as the investment rate assumption. The 70s were a high-inflation period that had a lasting impact on people’s choices. Right now, we’re being skewed by a low-rate, low-inflation environment. I’ll share an inflation case study next week. The impact of high inflation was better understood in the 80s than today.