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
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
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
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