Assume that five months from today you make the first of a series of quarterly deposits into an account earning an

APR of $4\mathrm{.}5\%$ with monthly compounding. Each deposit is $1\%$ larger than the last one and your final deposit occurs

two years and eight months from today. Four years and one month from today, you make your first semiannual

withdrawal from the account. The first withdrawal equals $$100$ and each subsequent withdrawal is $2\%$ smaller than

the previous one. Your final withdrawal will occur seven years and seven months from today. How large do you

need to make your first deposit so that you can make your planned withdrawals?

Note: If in any step you are solving for anything other than the left hand side of an equation, clearly state what you

are solving for.

must solve by hand, no excel