Calculating Remaining Loan with Differential Equation | DE Question Homework

[annoymage]

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

$$\frac{dS}{dt}$$ = $$\frac{S}{20}$$ - 12k

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

e^{$$\frac{-t}{20}$$}S = 12k(1-e^{$$\frac{-t}{20}$$}) + 19000

defenitely something is wrong,

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

$$\frac{dS}{dt}$$ form,

 

[annoymage]

FYI, its e^-t/20, sorry

 

[annoymage]

i've been told that.. bank usually are compound interest... i don't know what that means

 

[bobey]

looks like you have to submit the answer tomorrow, ait?

your answer should :
monthly repayments : RM 754.85
total interest payable : RM5290.92

where
loan amount = RM 40,000
interest rate = 5%
loan term = 5 yrs
repayments = monthly
repayments type = principal & interest

based on this calculator : http://www.banks.com.au/tools/calculator/loan-repayments/

come on BAGINDA, think faster... huhuhuhu