42 A woman inherited $356,000. As she had no immediate need for the money at the time she inherited, she decided to invest some or all of it on January 1, 201 n , with a goal of making the money grow to

$500,000 by December 31, 201n + 5. She is considering the investments in the following table.

RATE MATURES Fund A 7% December 31 (at the end of one year)

Fund B 16% December 31 (at the end of the second year after investment)

Fund C 24% December 31 (at the end of the third year after investment)

Fund D 32% December 31 (at the end of the fourth year after investment)

She wants to set up her investment strategy at the start of year 1. If she does not need to invest all of the inheritance to have $500,000 at the end of year 6, she will find another purpose for the remainder.

She may choose to place a sum of money in any or all of the investments available at the start of year 1.

From that point, however, all subsequent investments should come from the matured investments of previous years. To ensure that funds are spread over different investment choices, she does not want any single new investment in any year to be over

$120,000. (Note that prior investments in a fund do not count toward this limit.)

How much money will she have to invest on January 1, 201 n , to meet her goal of $500,000 at the end of the sixth year?