When determining how much interest will be paid over the lifetime of a loan, knowing how to calculate compound interest is critical. Different than simple interest, this type of interest can be considered the interest which accrues on top of accumulated interest and the initial principal of a loan – or the “future value” of a loan or deposit.
Compound interest is important to understand, as the total interest paid on a loan grows at a faster rate than that of simple interest. For individuals or businesses seeking loans for investments or purchases, calculating interest is a necessary part of comparing different loan options. Understanding this type of interest will also help individuals or businesses make sound investment decisions, as deposits can also accrue interest.
This article will illustrate the compound interest formula, how to calculate it step by step, and provide examples of how to apply it in various scenarios.
Definition
Compound interest is defined as the interest calculated based on the initial principal and all previously accumulated interest on a loan. This represents the future value of the principal and accumulated interest.
Also known as ‘compounding interest,’ compound interest is calculated through multiplying the starting principal by one plus the annual rate of interest raised to the power of the number of compounding periods minus one. The number and frequency of compounding periods varies based on the schedule of a loan and can vary anywhere between daily to annually. The number of compounding periods will significantly influence the accumulated interest of a loan.
What is Compound Interest
Formula
Compound interest is calculated through multiplying the initial principal of a loan by one plus the annual interest rate raised to the number of compounding periods minus one. Values in this formula include the loan principal, the nominal annual interest rate, and the number of compounding periods according to the loan’s frequency schedule.
CI = P[(1 + i)n – 1]
Where:
CI = compound interest
P = principal amount (for loan or investment)
i = nominal annual interest rate in percentage terms
n = number of compounding periods
How to Calculate
Calculate Step by Step
- Determine the principal, nominal annual interest rate, and number of compounding periods.
- Add one to the nominal annual interest rate and raise by the number of compounding periods.
- Subtract one from the product created through Step 2.
- Multiply the product of Step 3 by the loan principal.
Example
An individual needs a personal loan to pay for a major expense. They are evaluating a personal loan offer from their bank, which uses compound interest. This loan will be paid back in a lump sum due at the loan’s maturity.
Based on the information their bank provided, the individual was able to determine the following values:
Initial Loan Principal: $8,000
Nominal Annual Interest Rate: 6.5%
Number of Compounding Periods: Three Periods
Given this information, the individual can populate the formula as follows:
CI = P[(1 + i)n – 1]
Where:
CI = compound interest
P = principal amount = $8,000
i = nominal annual interest rate = 6.5%
n = number of compounding periods = 3
Such that:
CI = 8,000[(1 + 0.065)3 – 1]
After populating the formula with the relevant values, the individual can now solve for the nominal interest rate plus one raised to the number of compounding periods minus one:
CI = 8,000[(1 + 0.065)3 – 1]
CI = 8,000[(1.065)3 – 1]
CI = 8,000[(1.208) – 1]
CI= 8,000(0.208)
After completing this step, the individual can now determine that the principal amount of the loan will be multiplied by 0.208. The product of this will be the compound interest of the loan, as follows:
CI = 8,000(0.208)
Compound Interest = $1,664
Here we can see that the accumulated interest on this personal loan is $1,664. This represents the future value of interest that will accrue on the loan, based on the principal and accumulated interest.
When the individual pays this loan back, they will have to pay back the $8,000 of principal plus the $1,664 of interest. In total, the individual will pay $9,664 back to the bank at the end of the loan’s life. This shows how important it is for borrowers to calculate the accrued interest to make sure they can afford the loan in the long run.
Tips for Calculating
Tip Number 1:
The number of compounding periods will influence the interest of a loan significantly. The loan schedule for compounding periods can vary anywhere between daily to annually. The more compounding periods of a loan there are, the higher the total interest of a loan will be. When calculating the interest of a loan, make sure to consider the number of compounding periods of a loan and their impact on the total value of the loan.
Tip Number 2:
Compound interest represents the amount of interest which will be paid at the end of the number of compounding periods measured. If an individual has a loan with a high number of compound periods, they can use the formula to determine the amount of interest to be paid at various stages. For example, if an individual has a 30-year home loan which compounds annually, the individual can calculate the interest at various points of the loan. For 10 years of interest, the individual will use 10 compounding periods. For 20 years, the individual will use 20 compounding periods, and so on.
Tip Number 3:
Compound interest applies to both loans and investments. Certain investments accumulate interest over time, such as savings accounts or bank certificates of deposits (CDs). The concept of compound interest can also be applied to these deposits to help investors know how much their initial investment will grow over a period of time. Investors would populate the principal with the initial amount of their investment and complete the formula to determine how much interest would accrue on their investment over a given number of periods.
Calculators
Various calculators can be used to determine how much compound interest a loan or investment will accrue over a given number of compounding periods. These calculators are reliable and effective methods of quickly determining the amount of interest which will accrue on a deposit or loan.
The U.S. Securities and Exchange Commission offers a compound interest calculator specifically to determine how much an investment will grow over time accounting for interest. This calculator also considers how much the lump sum will grow based on any additional monthly contributions and the frequency of the compounding periods.
Takeaways
Compound interest represents the future value of interest a loan or deposit will accrue over a given number of compounding periods. This type of interest factors the initial principal and accumulated interest of a loan. The number of compounding periods significantly influences the amount of interest which will accrue.
Compound interest is important for individuals and businesses to understand if they can afford the total cost of a loan and what the total value of an investment will be in the future.
When calculating compound interest for a loan, be sure to use the loan’s principal in the formula. When calculating interest for an investment, be sure to use your initial investment amount in the formula.
