Table of Contents
Introduction to Compound Interest
Compound Interest – Definition: Compound interest is a financial term that describes the addition of interest to the principal balance of a loan or deposit. The principal balance is the original amount of the loan or deposit. The interest is the fee charged for borrowing money or for depositing money.
- The interest is usually quoted as a percentage of the principal balance. For example, a loan with an annual interest rate of 10% would have a monthly interest rate of 0.833%.
- The interest is compounded periodically. For example, a loan with an annual interest rate of 10% might compound monthly. This means that the interest is added to the principal balance once a month.
- The interest is also compounded on a cumulative basis. This means that the interest earned in a previous period is added to the principal balance for the next period.
The following example illustrates the calculation of compound interest.
- Assume that you borrow $1,000 at an annual interest rate of 10%. The interest is compounded monthly.
- After one month, the principal balance would be $1,010. The interest for the month would be $10. The total amount owed would be $1,020.
- After two months, the principal balance would be $1,021. The interest for the month would be $11. The total amount owed would be $1,032.
- After three months, the principal balance would be $1,032. The interest for the month would be $
S.I and C.I Formula Comparison
- The S.I. (standard deviation) formula is used to calculate the variability of a set of data. The C.I. (confidence interval) formula is used to calculate the range of values within which a population parameter is likely to fall, given a certain level of confidence.
- The two formulas are similar in that they both calculate a measure of variability or uncertainty. However, the S.I. formula is used to calculate the variability of a set of data, while the C.I. formula is used to calculate the range of values within which a population parameter is likely to fall.
Terms Related to Compound Interest
- Compound interest – The interest earned on an investment that is reinvested in addition to the initial investment.
- Simple interest – The interest earned on an investment that is not reinvested.
- Annual percentage yield (APY) – The effective annual rate of return on an investment, taking into account the effect of compounding.
- APR – The annual rate of interest on an investment.
Compound Interest Half Yearly Formula
A = P (1 + r/2)^{6}
Where:
A = the future value of the investment
P = the amount of the initial investment
r = the annual interest rate
6 = the number of periods per year
Compound Interest Examples
1. If you deposit $5,000 in a bank account that pays 5% interest compounded annually, how much money will you have in the account after five years?
You will have $5,625 in the account after five years.
Important Elements of calculating Compound Interest
The following are the key elements of compound interest:
- Principal: The original amount of money invested
- The original amount of money invested Interest Rate: The percentage of interest earned on the principal
- The percentage of interest earned on the principal Time: The number of years the money is invested
- The number of years the money is invested Compound Frequency: The number of times the interest is compounded per year
- The number of times the interest is compounded per year Present Value: The value of the investment at the present time
- The value of the investment at the present time Future Value: The value of the investment at a future time
- The value of the investment at a future time Total Amount of Interest: The total amount of interest earned over the life of the investment
- The total amount of interest earned over the life of the investment Payout: The total amount of money received after the investment matures
- The total amount of money received after the investment matures APR: The annual percentage rate, which is the equivalent interest rate per year
- The annual percentage rate, which is the equivalent interest rate per year EAR: The effective annual rate, which takes into account the compounding frequency
- The following is an example of how to calculate compound interest:
- If you invest $1,000 at a 5% interest rate, compounded annually, the future value after 5 years would be $1,261.54. This is calculated by multiplying
Frequency of Compounding
- The rate at which an amount increases is determined by the periodicity with which interest is compounded—daily, monthly, or annually. Make sure you understand how often interest compounds whether you take out a loan or create a savings account.
- Continuous Compounding: This is when interest compounds continuously, rather than at fixed time intervals. The math to calculate continuous compounding is a bit more complicated, but the principle is the same: the more often interest compounds, the faster your money grows.
