Example $8\mathrm{.}2\mathrm{.}3$: Outstanding balance on a car loan.

An individual takes out a $$20,000$ carloan. The annual interest rate for the loan is $3\%.$ He wishes to make a monthly payment of $$500.$ Define $a_n$ to be the amount of outstanding debt after $n$ months. Since the interest rate describes the annual interest, the percentage increase each month is actually $3\frac{\%}{12}=0\mathrm{.}25\%.$ Thus, the multiplicative faclor prorease each month is $1\mathrm{.}0025.$ The recurrence relation for $\{a_n\}$ is:

$a_0=$$$20,000$

$a_n=(1\mathrm{.}0025)*a_{n-1}-500$ for $n1$

The $(1\mathrm{.}0025$