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?
1 Answer
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[4] = (d + (1 + r)^4 (r s - d))/r = 462.36
pr[4] = (d - r s) (r + 1)^(4 - 1) = 142.42
interest payment in month 4 = d - pr[4] = 24.19
accpr[4] = (d - r s) ((1 + r)^4 - 1)/r = 537.64
interest payments up to month 4 = 4*d - accpr[4] = 128.80
Checking with Excel
Also, in Excel accpr[4] = 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[12] = (d - r s) ((1 + r)^12 - 1)/r = 755.92
interest payments up to month 12 = 12*d - accpr[12] = 8471.00
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1I have added a section specific to the TI-84's finance functions. Jun 26, 2020 at 16:09