Abstract: This article will analyse how to calculate the loan repayment in mathematically and programming totally.
Question
Firstly, let us display the question:
Alice borrows £1000, the year rate is 7.0% and repayment term is 3 years, So how much Alice need to repay every month?
This question is a simple example for Loan or Mortgage repayment calculation. If you understand how to answer this question, you will understand the repayment theory easily.
Type of yearly interest
Interest is defined as the cost of borrowing money as in the case of interest charged on a loan balance. Conversely, interest can also be the rate paid for money on deposit as in the case of a certificate of deposit.
Generally, Interest can be calculated in two ways: Simple Interest and Compound Interest.
Simple Interest
The reason calls it simple is that it only calculated on the principal, or original, amount of a loan without calculating the interest of the interest.
1 | Simple Interest = Principal * Interest Rate * Term of the loan |
COMPOUND INTEREST
When the money you borrow generates interest, the interest will also generate the internet. So this type of interest is so complex. Compound interest is calculated on the principal amount and also on the accumulated interest of previous periods, and can thus be regarded as “interest on interest.”
Yearly vs Monthly
In general, the annual internet is published. However, the repayment is by monthly usually. So it is necessary to convert yearly interest to monthly interest. See this article.
This website is a convert to do this work.
Basically, we will think about just divide the yearly interest to 12 and get the monthly interest in intuitive. But it is not the precise internet. Because we still need to think about the internet can generate interest.
So when we do the convert, we need to think about the next month rate will be based on more present value.
Assume we have principal $P$, then yearly interest is $y$ and monthly interest is $m$. So we will use the final principal and interest as a bridge to construct an equation:
so the function to convert yearly interest to the monthly internet is as follows:
Repayment Calculate
The final month repayment formula
Please check this handwrite note to review how to deduce this formula.
Terminology
Principal: Principal is a term that has several financial meanings. The most commonly used refers to the original sum of money borrowed in a loan or put into an investment. Similar to the former, it can also refer to the face value of a bond.
Compound interest: Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.
Simple interest: Simple interest is a quick method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.
Future Value: Future value is the value of an asset at a specific date. It measures the nominal future sum of money that a given sum of money is “worth” at a specified time in the future assuming a certain interest rate, or more generally, the rate of return; it is the present value multiplied by the accumulation function.
Present Value: PV is the current worth of a future sum of money or stream of cash flows given a specified rate of return.