# Calculating Remaining Loan with Differential Equation | DE Question Homework

• annoymage
In summary, the conversation discusses a recent graduate who borrowed $19,000 at an annual rate of 5% to buy a car from a bank. The graduate has made an arrangement to pay the bank a certain amount per month. The balance due on the loan, measured in years, is represented by the function S(t). The task is to write a differential equation to calculate the amount of loan left to be paid. The proposed solution is \frac{dS}{dt} = \frac{S}{20} - 12k. However, it is suspected to be incorrect as an explicit solution of S shows that something is wrong. The conversation also mentions that banks usually use compound interest, and the answer is needed by tomorrow. #### annoymage ## Homework Statement A recent graduate borrowed 19000$ 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.

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,

FYI, its e-t/20, sorry

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

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

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

## What is a differential equation?

A differential equation is a mathematical equation that relates a function to its derivatives. It is used to describe the rate of change of a variable over time. In the context of loans, a differential equation can be used to calculate the remaining loan amount over time.

## How do you use differential equations to calculate remaining loan?

In order to calculate the remaining loan amount using differential equations, you will need to know the initial loan amount, interest rate, and the time period. You will also need to determine the appropriate differential equation based on the type of loan (e.g. fixed or variable interest rate). Once you have this information, you can use the differential equation to solve for the remaining loan amount at any given time.

## What are the limitations of using differential equations to calculate remaining loan?

There are a few limitations to using differential equations in loan calculations. One limitation is that it assumes a constant interest rate, which may not always be the case in real-life loans. Additionally, it does not take into account any additional fees or charges that may be associated with the loan. It is also important to note that the calculated remaining loan amount is an approximation and may not be completely accurate.

## Can differential equations be used for all types of loans?

While differential equations can be used for many types of loans, they may not always be the most accurate method. For more complex loans with changing interest rates or variable payments, other methods may be more appropriate. It is important to understand the limitations and assumptions of using differential equations for loan calculations.

## What are some real-world applications of using differential equations in loan calculations?

Differential equations can be used in various real-world scenarios, such as calculating mortgage payments, car loans, or student loans. They can also be used in financial planning and budgeting to estimate the remaining loan amount over time. Additionally, differential equations can be used in analyzing and predicting the impact of changes in interest rates on loan repayments.