# What is the difference between Simple Interest and Compound Interest?

Published on: 28 December, 2022

When creating or tracking an agreement on Pigeon, you are given the option to choose between the two most common methods of adding interest to your loan: Simple Interest or Compound Interest.

Reminder 💡: Interest can be thought of as the price paid by the Borrower to the Lender in exchange for the right to borrow money, and is usually calculated as a percentage of the loan amount (a.k.a. the principal).

Simple Interest

Simple Interest calculates the cost of borrowing based on the original principal amount at the beginning of the loan, and does not take into consideration the effects of compounded or "accrued" interest over the duration of the loan. Using this method can be thought of as calculating the total amount of interest to be paid to the Lender up front, and then adding it to the Principal to be paid over the course of the loan.

Unlike Compound Interest, Simple Interest is calculated once at the initiation of the loan, and does not change or "update" based on the outstanding balance at the end of each repayment period (after any of the Borrower's payments have been applied, of course).

Therefore, the total amount of interest paid to the Lender is known from the beginning and will not increase or decrease based upon the Borrower's repayment behavior (e.g. Borrowers won't pay less for paying off their loan early, nor will they pay more for missed or late payments).

The Simple Interest Formula utilized on the Pigeon platform is A = P(1+(R/12)t), where:

• A = Total Loan Value (Principal + Interest)
• P = Principal
• R = annual interest rate expressed as a decimal (e.g. 5% annual interest = .05)
• t = number of months of loan

Simple Interest Example: Sandra agrees to lend Jason \$10,000 for 24 months with an annual interest rate of 5% per year, and selects the "Simple Interest" option. Using the formula above, we can determine that Jason can expect to pay her back a total of A = \$10,000(1+(.05/12)*24) = \$11,000. If split into 24 equal monthly payments, he would pay back (\$11,000/24) = \$458.33 per month, with a total borrowing cost of \$1000 paid to Sandra for lending him the money. This \$1000 borrowing cost will not fluctuate regardless of whether he pays back the loan early, late, or on time.

Compound Interest

Compound interest, sometimes described as "interest on interest," is a calculation method used across a wide range of financial products from personal loans and credit cards all the way to government-issued bonds and business lines of credit. Compound Interest takes into account the previous period's interest and/or repayment activity when determining the amount of interest due for each upcoming period.

Unlike loans with Simple Interest, the borrowing cost paid to the Lender for loans with Compound Interest may increase or decrease throughout the lifetime of the loan depending on how much the borrower pays back (or fails to pay back) for each period of the loan. For example, many credit card users are aware that if they pay their balance off immediately, they will end up paying a lot less interest than they would if they skipped 6 months of payments.

The Compound Interest formula used on Pigeon follows a fixed monthly loan amortization schedule (i.e. with equal monthly payments of principal + interest, compounded monthly) calculated as PMT = [PVi(1+i)^n] ÷ [(1+i)^n - 1], where

• PMT = Monthly Loan Payment (includes repayment of Principal + Interest)
• PV = present value of the loan at initiation (e.g. the Principal)
• i = monthly interest rate expressed as a decimal (e.g. for a loan charging 5% interest per year, i = .05/12 = .004167)
• n = number of months of loan

Compound Interest Example: Sandra agrees to lend Jason \$10,000 for 24 months with an annual interest rate of 5% per year, and selects the "Compound Interest" option. Using the formula above, we can determine that Jason can expect monthly payments of PMT = [\$10,000*.004167*(1.004167)^24] ÷ [(1.004167^24)-1] = \$438.71 per month. Assuming Jason makes all of his 24 monthly payments on time in the month they are due, he can expect to pay Sandra back a total of \$10,529.13, for a total borrowing cost of \$529.13. However, the amount of interest he will pay to Sandra will decrease if he pays off his loan early (i.e. he pays back more than is due each month). If he misses payments or falls behind on his loan, he will end up paying more interest to Sandra over the course of the loan.