Option $2$: Deposit regular monthly payments into an investment account. The Formula for finding the accumulated amount in a savingslinvestment account with regular monthly payments deposited is:

i$.$ John doesn't have enough to make a one$-$time deposit, but he can make monthly payments into a retirement account. Suppose John makes $$125$ monthly payments into an account with a rate of return of $9\mathrm{.}8\%.$ How much would he have at age $50?$

ii$.$ If John were to increase his monthly deposit amount to $$200$ monthly, how old $($to the nearest year$)$ would John be when the balance reaches $$1,000,000?$

iii. What monthly deposit amount would be required for John to get to $$1,000,000$ by age $50?$

How much money would John actually have invested under these circumstances?

How much interest would have been earned in that time?

iv$.$ What if John decided to wait until age $60$ to retire? In other words, if he made the same payments found in part iii above, how much would be in his account at that time? Is that total more than, less than, or equal to what you would expect? Give an explanation as to why you believe that is the case.