Question n$.1$

a$)$ You plan to pay $$150$ at the end of each week for the first $5$ years, $$1,000$ at the end of each

quarter for the next $10$ years and $$2,000$ at the end of each semester for the last $5$ years into an

account that will earn:

Years

$1$ to $5$: $4\mathrm{.}8\%$ annual nominal, capitalized monthly.

$6$ to $10$: $6\%$ annual nominal, capitalized semi$-$annually.

$11$ to $20$: $8\%$ annual nominal, capitalized quarterly.

How much will you have in this account in $20$ years?

b$)$ What amount invested today, in an account earning $6\%$ effective annual return for the first $4$

years and $9\%$ nominal annual return, capitalized monthly, thereafter, would allow withdrawals of

$$3,000$ per quarter for the first $7$ years and $$1,500$ per month for the next $8$ years $($end of

periods$),$ assuming a zero balance at the end of year $15?$