personal finance
posted by susie on .
if you wanted to save $ 50,000 to have it available in 20years provided the investment would return an APR of 12% compounded monthly.
a. how much would you need to have at the beggining (lump sum) in order to achieve the mark of $50,000.
b. how much would you have to save every year for 20 years?
c. how much would you have to save for the first 10years and nothing more?

For (a), solve the compound growth formula
X*(1.12)^20 = 50,000
X wil be the answer
For (b), use the calculation tool at
http://www.collegegold.com/calculatecost/savingsgrowthprojector
I get 619.59 per year
For (c), first calculate how much you need after 10 years to reach 50,000 with compound interest, without contributing for the last 10 years. Then use the computation tool of (b) to determine how much you must save per year for the first 10 years 
a) amount = princ(1+i)^n
50000 = princ(1.01)^240
princ = 4590.29
b) amount = payment((1 + i)^n 1)/i
50000 = payment(1.01^240  1)/.01
payment = 50.54 per month.
c) so you are depositing every month for 10 years, then letting it "ride" for the next 10 years ?
50000 = [payment(1.01^120  1)/.01](1.01^120
50000 = payment(230.0386895)(3.300386895)
payment = 65.56 
I didn't read the problem carefully, and assumed interest compounded annually.
Kudos to Reiny for doing it right, and knowing the formula for (b).