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## Homework Statement

A recent graduate borrowed 19000$ at an annual rate of 5%

to buy a car from a bank. Suppose that it has made an arrangement to pay the bank

r $ per month. Let S(t), measured in $, be the balance due on the loan at ant time

t, measured in years.

Write a differential equation to calculate the amount of loan left to be

paid.

## Homework Equations

n/a

## The Attempt at a Solution

[tex]\frac{dS}{dt}[/tex] = [tex]\frac{S}{20}[/tex] - 12k

i think this is wrong because something is wrong when i do an explicite solution of S

e

^{[tex]\frac{-t}{20}[/tex]}S = 12k(1-e

^{[tex]\frac{-t}{20}[/tex]}) + 19000

defenitely something is wrong,

can someone help me how to translate or give some clue the question to

[tex]\frac{dS}{dt}[/tex] form,