What $5 a day becomes in 40 years at 7%, solved step by step

Problem. You set aside $5 every day, which is $1,825 a year, and invest it once a year at the end of each year for 40 years. Assume an average return of 7% a year, with the growth compounding every year. What is the total after 40 years?

Step by step

1. Find the yearly amount: 5 × 365 = 1,825, so you invest $1,825 a year.

2. Use the future value formula for equal yearly deposits: FV = deposit × ((1 + r)^n − 1) / r, where r = 0.07 and n = 40.

3. Work out the growth factor: 1.07^40 ≈ 14.97.

4. Subtract 1: 14.97 − 1 = 13.97.

5. Divide by the rate: 13.97 ÷ 0.07 ≈ 199.6. This number tells you how many yearly deposits the pot is worth after 40 years of growth.

6. Multiply by the deposit: 1,825 × 199.6 ≈ 364,000, so the pot is about $364,000.

7. Find what you paid in: 1,825 × 40 = 73,000, so you put in $73,000 of your own money.

8. Find the growth: 364,000 − 73,000 = 291,000, so about $291,000 of the total is investment growth.

Answer: Investing $5 a day for 40 years at an average 7% a year gives 1,825 × ((1.07^40 − 1) / 0.07) ≈ $364,000, of which you put in $73,000.

The 7% a year is an assumed average, not a guarantee, and real returns vary from year to year and are not adjusted here for inflation, fees or taxes.