You are saving for retirement. To live comfortably, you decide you will need to

save $$1,400,000$ by the time you are age $67.$ Today is your $25$ th birthday, and

you decide, starting today and continuing on every birthday up to and

including your $67$ th birthday, that you will put the same amount into a savings

account. If the interest rate is $10\%,$ you set aside $$2,363\mathrm{.}27$ each year to

make sure that you will have $$1,400,000$ in the account on your $67$ th birthday.

You realize that your plan has a flaw. Because your income will increase over

your lifetime, it would be more realistic to save less now and more later.

Instead of putting the same amount aside each year, you decide to let the

amount that you set aside grow by $8\%$ per year. Under this plan, how much

will you put into the account today? $($Recall that you are planning to make the

first contribution to the account today.$)$