David has decided to retire once he has $$1,500,000$ in his retirement account. At the end of each year, he will contribute $$7,000$ to the account, which is expected to provide an annual return of $7\mathrm{.}0\%.$ How many years will it take until he can retire?

$41$ years

$37$ years

$40$ years

$32$ years

$39$ years

Suppose David$$s friend, Ben, has the same retirement plan, saving $$7,000$ at the end of each year and retiring once he hits $$1,500,000.$ However, Ben$$s account is expected to provide an annual return of $9\mathrm{.}4\%.$ How much sooner can Ben retire?

$6$ years

$4$ years

$5$ years

$8$ years

$7$ years

After $25$ years, neither David nor Ben will have enough money to retire, but how much more will Ben$$s account be worth at this time?

$$107,938$

$$186,514$

$$141,056$

$$289,671$

$$162,869$

David is jealous of Ben because Ben is scheduled to retire before him, so David decides to make whatever end$-$of$-$year contribution is necessary to reach the $$1,500,000$ goal at the same time as Ben. If David continues to earn $7\mathrm{.}0\%$ annual interest, what annual contributions must he make in order to retire at the same time as Ben?

$$13,361$

$$8,226$

$$7,751$

$$11,695$

$$13,241$