Compound Interest If you want to find n, the number of years, enter values for FV, P and r.  Don't forget to change c, compounds per year. FV = P(1 + i)kn Formula from book where  i = r ÷ k Example: 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?  (before taxes) We need to find i  and  n ... i  =  i = r ÷ k  = 0.11/4 = 0.0275   P = present Value = 20,000  n  = number of years = 30  k  = 4 quarterly means 4 times a year We want to find FV = Future value FV =  P(1 + i)n  = 20,000×(1 + 0.0275)120   = 20,000× 25.93102392  = 518,620.48 Try the calculator below.  Use P = present value = 20000 r = rate = .11, t =years = 30, c = compound periods = 4 Leave the F  blank. This is a Compound Interest calculator. Do not use commas or dollars signs in textboxes. FV  = =  future value P = = present value r  = = interest rate per year n = = number  of years k = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 365 = compounds per year  monthly = 12, quarterly = 4 ANSWER: You must enter values in 3 out of the 4 textboxes. If you get NaN in the answer box , check your input values.  FV should be more than P .  Interest rate should be between 0 and 1.  Years can be partial years i.e. 1 and a half years = 1.5

Annuities or Amortization
The present value A and the rent  R of a decreasing annuity of n × k   payments (rent) compounded at a rate i  per interest period.
Also called amortization when the payments are equal and at a regular time interval. (car loans and home mortgages )

James buys a house for \$90,000.  He puts \$10,000 down and then finances the rest at 9% interest compounded monthly for 25 years.

Find his monthly payments
This is a Present Value of an Annuity problem. We need to find the Payment P
 Formula from book where  i = r ÷ t  and k = t × c Note: k = 12, n = 25,  i = .09/12 = .0075 and A = 90,000 - 10,000 = 80,000 The monthly payments are \$671.36

Find the total amounts he pays for the house.

You pay \$10,000 down and \$671.36 a month for 25 years
10,000 + 671.36 × 12 × 25 = 10,000 + 201,408 = 211,408
You pay \$211,408 for the house with interest.

 Try the calculator below.  Use A = present value = 80000 r = rate = .09, n =years = 25, k = compound periods = 12 Leave the F  blank. This is a Annuity - Amortization calculator. Do not use commas or dollars signs in textboxes. P  = = payment (or R  for rent) A  = = present value (or PV) r   = = interest rate per year n  = = number  of years k  = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 365 = compounds per year    monthly = 12, quarterly = 4 ANSWER: You must enter values in 3 out of the 4 textboxes. If you get NaN in the answer box , check your input values.   Interest rate should be between 0 and 1.  Years can be partial years i.e. 1 and a half years = 1.5
 Ti-83 TVM  Time Value of Money The Ti-83 has finance functions.  In the Ti-83plus, the finance functions are located in the Apps (applications) menu. You can download other functions for the Ti-83plus. You want to purchase a home for \$150,000 with a traditional 30 year loan with monthly payments at the end of each month. What is your monthly payment at 8% compounded monthly?   How much would you pay for the house? Press   2nd FINANCE  1 ENTER N = 12 × 30 = 360   Number of payments I % = 8  means 8 % no decimal for TVM needed PV = 150000 is Present Value PMT payment or rent is unknown FV = 0 Future Value is zero when loan is paid off P/Y and C/Y = 12 payments and compound periods per year PMT: END most loans compound the interest at the end of the month, Press  2nd QUIT 2nd FINANCE 2 (tvm_Pmt) Your payment (or rent) would be \$1,100.64.  12 months × 30 years = 360 payments You pay 360 × 1,100.64 = \$396,230.40 for the house.  Use your calculator or the Annuity Calculator above to find the monthly payment at 7%.  The monthly payment is \$997.95.   You pay 360 × 997.95 = \$359,262.00 for the house.  That is about a \$37,000 dollar savings.

Tutorials and Applets by
Joe McDonald
Community College of Southern Nevada