Compound Interest -- Section 9.1 --

 Compound Interest: Future Value FV = PV(1 + i)kn   where Compound Interest: Present Value PV = FV(1 + i)-kn    = FV ÷ (1 + i)kn  where FV = Future Value PV = Present Value or Principal  i =  r ÷ k,  r = annual rate, k = number of periods per year n = number of years

Compound Interest and Annuities Click  for Calculator

 You want to invest \$20,000 for 30 years  at 11 % interest compounded quarterly.  How much money will you have at the end of the 30 years?
 Solve Step i = 0.11 ÷ 4 = 0.0275 k = 4, r = 0.11, Quarterly means 4 times a year FV = PV(1 + i)kn FV = 1,000,000, n = 30 years FV = 20,000(1 + 0.0275)4(30) Find the Future Value FV = 20,000(1.0275)120 » 518,620.48 You would have \$518,620.48 after 30 years. (before taxes) Hint: don't round until you are completely finished with your calculations.

 You want to invest \$10,000 for 20 years  at 10 % interest compounded quarterly.  How much money will you have at the end of the 20 years?
 [Solution]
 Let's say you want to retire in 30 years with a million dollars.  You invest some money in a mutual fund that expects to earn an average of 12% per year compounded monthly.  How much money do you need to invest?
 Solve Step i = 0.12 ÷ 12 = 0.01 k = 12, r = 0.12, Monthly means 12 times a year PV = FV(1 + i)-kn    = FV ÷ (1 + i)kn Find the Present Value PV = 1,000,000 ÷ (1 + 0.01)12(30) PV = 20,000, n = 30 years PV = 1,000,000 ÷ (1 .01)360 »  27,816.69 You would have to invest \$27,816.69 to earn a million dollars after 30 years. (before taxes) Enter 1000000 ÷ (1 + 0.12 ÷ 12) xy  (12 × 30) [enter or =] in your calculator Hint: don't round until you are completely finished with your calculations.

 Let's say you want to retire in 20 years with a million dollars.  You invest some money in a mutual fund that expects to earn an average of 8% per year compounded monthly.  How much money do you need to invest?
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