# Calculating interest and Principal Paid using TI-84

How do I calculate the net quantity of interest on a loan, and the net quantity of the principal on the loan, that I have paid off after a given number of payment periods in the finance app on a TI-84 graphing calculator?

The general formulae are straightforward to program.

Using formulae derived in this answer . . .

``````p[n] = (d + (1 + r)^n (r s - d))/r

pr[n] = (d - r s) (r + 1)^(n - 1)

accpr[n] = (d - r s) ((1 + r)^n - 1)/r
``````

where

``````p[n] is the principal remaining in month n, i.e the balance
pr[n] is the principal repayment in month n
accpr[n] is the accumulated principal repaid in month n

s is the initial loan principal
r is the monthly interest rate i.e. nominal annual rate ÷ 12
d is the regular monthly payment
``````

For example, a loan with a 7 month term `t`

``````s = 1000
r = 0.04
t = 7
d = (r (1 + r)^t s)/((1 + r)^t - 1) = 166.61
``````

The principal and interest payments in month 4

``````p = (d + (1 + r)^4 (r s - d))/r = 462.36

pr = (d - r s) (r + 1)^(4 - 1) = 142.42

interest payment in month 4 = d - pr = 24.19

accpr = (d - r s) ((1 + r)^4 - 1)/r = 537.64

interest payments up to month 4 = 4*d - accpr = 128.80
``````

Checking with Excel Also, in Excel `accpr = 537.64` can be calculated using

``````=CUMPRINC(0.04,7,1000,1,4,0)
``````

TI-84 Method from the manual page 259 The formula matches the TI-84 example, albeit a slight precision difference.

``````s = 100000
r = 0.085/12
d = 768.91

accpr = (d - r s) ((1 + r)^12 - 1)/r = 755.92
interest payments up to month 12 = 12*d - accpr = 8471.00
``````
• I have added a section specific to the TI-84's finance functions. – Chris Degnen Jun 26 at 16:09