Ted has been dollar cost averaging in a mutual fund by investing $1,500 at the beginning of every quarter for the past 5 years. He has been earning an average annual compound return of 9% compounded quarterly on this investment. How much is the fund worth today

$38,208.04

Explanation:

The amount is constant which means that it is an annuity.

It is based on the past so to find the value today, take the future value of the annuity from 5 years ago to find out the value today.

As this is paid at the beginning of the period, it is an annuity due.

Future value of annuity due = Annuity * (1 + r) * ( ( 1 + r)^n - 1 / r)

Rate = 9%/ 4 quarters = 2.25%

Periods = 5 * 4 quarters = 20 periods

Future value of annuity = 1,500 * (1 + 2.25%) * ( ( 1 + 2.25%)²⁰ - 1 / 2.25%)

= $38,208.04

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