$1.$ Stone Inc. deposits $$40,000$ today into a special fund that is needed at the end of six years.Answer $1$

A financial institution serves as the fund trustee and pays $10\%$ interest on the fund balance.

Compute the fund balance at the end of year $6$ assuming annual compounding.

$2.$ On January $1$ of the current year, Southwest Inc. adopts a plan to accumulate funds forAnswer $2$

environmental improvements to occur $4\mathrm{.}5$ years in the future, at an estimated cost of $$2,000,000.$

Southwest plans to make four equal annual deposits in a fund that earns interest at $10\%$

compounded annually. The first deposit is made on July $1$ of the current year. Compute the

amount of the annual deposit.

$3.$ Hanks Inc. establishes a debt retirement fund to retire debt of $$72,820.$ Hanks makes three equalAnswer $3$

annual contributions of $$20,000,$ starting on January $1$ of the current year. The fund earns interest

at $10\%,$ compounded annually. The $$72,820$ debt must be paid on December $31,$ three years later.

What is the balance of the fund at December $31$ in three years?

$4.$ Gold Inc. invests $$10,000$ today in a mutual fund. Gold anticipates leaving this fund alone for $12$ years.Answer $4$

The fund is increased each year$-$end by specified compound interest rates as follows: years $1$ to $4$

inclusive,$8\%$; $5$ to $8$ inclusive, $9\%$; and $9$ to $12$ inclusive, $10\%.$ Compute the fund balance at the

end of year $12.$