finite math
posted by distressed .
A young executive deposits $400 at the end of each month for 7 years and then increases the deposits. If the account earns 7.2%, compounded monthly, how much (to the nearest dollar) should each new deposit be in order to have a total of $400,000 after 25 years

Split the problem in two parts, 25 years and 18 years.
The interest rate is known for the first part (7% p.a. or per month?) and compounded monthly. So the future value after 25 years is determined, say A.
Assuming A<400,000=target, subtract
remaining future value B=400,000A and calculate deposit required for 18 remaining years at the given interest rate.
For the second part, the future value after (a further) 18 years is known, 
Suppose a state lottery prize of $2 million is to be paid in 20 payments of $100,000 each at the end of each of the next 20 years. If money is worth 9%, compounded annually, what is the present value of the prize?

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