Question

Many argue that investors should invest at the beginning of the year rather than at the end. What is the difference in your retirement account if you invests $3,000 per year at 10 percent over a 30-year period?

Answer 1

If investment was done at the end of every year:

Future value = Annuity * [(1 + r)ⁿ - 1] / r

Future value = 3,000 * [(1 + 0.1)³⁰ - 1] / 0.1

Future value = 3,000 * 164.494023

Future value = $493,482.07

If investment was done at the beginning of every year:

Future value = (1 + r) * Annuity * [(1 + r)ⁿ - 1] / r

Future value = (1 + 0.1) * 3,000 * [(1 + 0.1)³⁰ - 1] / 0.1

Future value = 1.1 * 3,000 * 164.494023

Future value = $542,830.28

Difference = $542,830.28 - $493,482.07

Difference = $49,348.21