Loans are a regular part of our lives, whether it’s for purchasing a car, a house, or even electronics. They help ease our financial burden to some extent. However, it’s important to understand that loan repayment methods can vary. Some loans follow equal principal repayment, while others use equal installment payment. What do these terms mean, and how do they affect your debt? Let’s explore the details today!

\(Principal_{t} = \frac{Loan\ amount}{Loan\ period}\)

\(Interest_{t} = Outstanding\ Balance_{t-1} \times i\)

\(Total\ Payment_{t} = Interest_{t} + Principal_{t}\)

Let’s take an example: The loan amount is $10,000, with an annual interest rate of 5% and a loan period of 10 years. We make equal principal payments each time.

We can obtain the Amortization Schedule_1 below:

This is a Stacked Chart showing the Total Payments, Interest Payment, and Principal Payment for each period.

\(Total\ Payment_{t} = \frac{Loan\ amount }{\frac{1- (\frac{1}{1+i})^n}{i}}\)

\(Interest_{t} = Outstanding\ Balance_{t-1} \times i\)

\(Principal_{t} = Total\ Payment_{t} - Interest_{t}\)

Let’s take the same example: The loan amount is $10,000, with an annual interest rate of 5% and a loan period of 10 years. We make equal installment payments each time.

We can obtain the Amortization Schedule_2 below:

This is also a Stacked Chart showing the Total Payments, Interest Payment, and Principal Payment for each period.

We can compare them on the one page:

Let’s take a look at the comparison table for the total amount.

Let’s see more clear.

We can obtain that:

1. In the equal principal payment method, the total repayment amount decreases over time because the remaining principal decreases, resulting in less interest being generated.

2. In the equal installment payment method, the total repayment amount stays the same each period. As the outstanding principal decreases, the interest payment also decreases, causing a higher proportion of each payment to go towards repaying the principal.

Given the same loan term and interest rate, the equal installment payment method accrues more interest compared to the equal principal payment method. If you want to minimize your payments to the lender, you might prefer the equal principal payment method. However, if you prioritize a steady cash flow to ease your financial burden, you might opt for equal installment payments since they initially require a heavier repayment load.

This my R code for Comparison Plot 1:
p1_plotly<-ggplotly(p1)                         #change the format
p2_plotly<-ggplotly(p2)                         #change the format
subplot(p1_plotly, p2_plotly,shareY = TRUE)%>%  #use function
  layout(                                       #design the layout
  title = "Level Principal VS Level Payments",
  xaxis = list(title = "Time"),
  yaxis = list(title = "Total_Payments"),
  legend = list(tracegroupgap = 0),
  annotations = list(                          #design the annotation
  list(
      x = 0.5,
      y = 1.05,
      xref = "paper", 
      yref = "paper",
      text = "Payments for interests and principal",
      showarrow = FALSE,
      font = list(size = 12, color = "black"))))