You are evaluating two annuity investments using a discount rate of $10\%$ p$.$a$.$:

Annuity $1-$ This annuity has $8$ quarterly payments in advance, growing at $1\%$ every $3$ months. The first payment is $$500.$ The value of this annuity today is: Blank $1$ Question $3$

Annuity $2-$ This annuity pays $$40$ every week for $2$ years. The value of this annuity today is: Blank $2$ Question $3$

You are asked to pay $$3,000$ to buy any one of the investments. Which investment will you buy $($if any$)?$ Answer: Blank $3$ Question $3$

$.$ Calculate the gain. Answer: