Compound Interest Calculator | Annuity Calculator | Ti-83 TVM Solver

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 =  = 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  = 

 = 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