Jonathan Clements | July 21, 2018

**FORGET XBOX** and PlayStation. If you’re an investment nerd, nothing beats playing with a financial calculator, especially running scenarios that combine dollars, investment returns and great gobs of time. Here are six mathematical musings—not all of them happy:

- Got a newborn daughter or granddaughter? If you invest $1,000 on her behalf and the money notches 6% a year, she’ll have almost $106,000 at age 80. That 6% is my assumption for long-run annual stock returns. But that 6% also assumes 2% inflation—and 2% inflation for 80 years would slash the spending power of that $106,000 to $21,700. That’s not as impressive, but it isn’t bad.
- If you buy actively managed stock funds, you’re likely to lag behind the market by some 1.5 percentage points a year. Result: Instead of earning the 6% annual return you’d collect if you bought index funds with rockbottom annual expenses, you might notch 4.5%. Now, imagine you socked away $5,000 a year for 40 years. Active funds would leave you with $559,000, versus $820,000 if you indexed.
- Suppose you entered the workforce at age 22 and saved $1,000 a month for the next 10 years. Assuming 6% investment returns, you’d have close to $165,000 at age 32. What if you then stopped saving, but left the money to keep growing? At age 70, you would have $1.5 million, or $583,000 after adjusting for 48 years of 2% annual inflation. That would be enough to generate $23,300 a year in retirement income, figured in today’s dollars and assuming a 4% portfolio withdrawal rate.
- Imagine you socked away $100—and somehow ensured it remained untouched and untaxed for 250 years. Using the above investment and inflation assumptions, your heirs or designated charity would have $212 million, or $1.5 million after adjusting for inflation.
- Time is our ally when we invest, but it’s our enemy when we’re in debt. Want to limit the damage? Let’s say you took out a 30-year, fixed-rate $300,000 mortgage costing 4.5%. Your monthly principal-and-interest payment would be $1,520. What if you put an extra $480 every month toward paying down the principal, so you were sending the mortgage company $2,000 a month? You’d drastically reduce the interest charges you incurred—and pay off the mortgage in 18 years and five months.
- Imagine you racked up $5,000 in credit card debt while in college. You never paid down the balance and, indeed, the credit card company let you add the 20% annual interest to the account balance. After 40 years, you’d receive a credit card statement showing more than $7.3 million owed.

Don’t own a financial calculator? You can do most of the above calculations with the Investment Returns calculator at Dinkytown.net and the Mortgage Calculator at Bankrate.com. Want to read more about compounding? Check out our money guide’s chapter on investment math, as well as The Tipping Point, one of HumbleDollar’s most popular blogs in 2018.

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