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Pre-Algebra
Table of Contents
Unit 6 Overview: Percents
6.1 Understand Percent
6.2 Solve General Applications of Percent
6.3 Solve Sales Tax, Commission, and Discount Applications
6.4 Solve Simple Interest Applications
6.5 Solve Proportions and their Applications

➕pre-algebra review

6.4 Solve Simple Interest Applications

Citation:

Simple interest is a fundamental concept in finance, used to calculate earnings or costs on investments and loans. It's a straightforward way to determine how much money grows over time, based on the initial amount, interest rate, and duration.

Understanding simple interest applications helps in making informed financial decisions. Whether you're saving money, taking out a loan, or investing, knowing how to calculate interest can give you a clear picture of your financial situation and potential outcomes.

Simple Interest Applications

Simple interest formula calculations

  • Simple interest formula $I = Prt$ calculates interest earned
    • $I$ interest earned
    • $P$ principal or initial amount invested or borrowed
    • $r$ annual interest rate as a decimal (5% = 0.05)
    • $t$ time in years
  • Find interest earned by multiplying principal, annual interest rate, and time in years ($1,000 principal, 5% rate, 3 years: $1,000 \times 0.05 \times 3 = $150 interest)
  • Find principal by dividing interest by product of annual interest rate and time in years
    • $P = \frac{I}{rt}$ ($150 interest, 5% rate, 3 years: $\frac{150}{0.05 \times 3} = $1,000 principal)
  • Find annual interest rate by dividing interest by product of principal and time in years
    • $r = \frac{I}{Pt}$ ($150 interest, $1,000 principal, 3 years: $\frac{150}{1,000 \times 3} = 0.05$ or 5% rate)
  • Find time in years by dividing interest by product of principal and annual interest rate
    • $t = \frac{I}{Pr}$ ($150 interest, $1,000 principal, 5% rate: $\frac{150}{1,000 \times 0.05} = 3$ years)

Real-world financial applications

  • Simple interest commonly used in savings accounts, certificates of deposit (CDs), and short-term loans
  • Savings account: principal is initial deposit, interest rate is annual percentage yield (APY), time is investment duration
  • Loan: principal is amount borrowed, interest rate is annual percentage rate (APR), time is loan duration
  • Example: $5,000 borrowed at 6% APR for 2 years, interest paid is $5,000 \times 0.06 \times 2 = $600
  • Investment yield can be calculated using the simple interest formula to determine the return on investment

Time unit conversions for interest

  • Interest rates typically expressed as annual rates, but time in simple interest formula must be in years
  • Convert months to years by dividing number of months by 12 (6 months = $\frac{6}{12}$ = 0.5 years)
  • Convert days to years by dividing number of days by 365 or 360 for some financial institutions (90 days = $\frac{90}{365}$ ≈ 0.247 years)
  • For interest periods shorter than a year, express time as fraction of a year
    • Example: investment earns 2% simple interest every quarter (3 months), calculate interest earned after 2 quarters using $t = \frac{2 \times 3}{12} = 0.5$ years in simple interest formula

Advanced Interest Concepts

  • Compound interest: interest is calculated on the initial principal and accumulated interest from previous periods
  • Present value: the current value of a future sum of money, given a specified rate of return
  • Future value: the value of an asset or cash at a specified date in the future, based on an assumed growth rate
  • Amortization: the process of spreading out a loan into a series of fixed payments over time

Key Terms to Review (20)

Interest Rate: The interest rate is the amount charged, expressed as a percentage of the principal, by a lender to a borrower for the use of assets. It is a key factor in financial calculations and applications involving loans, investments, and other financial instruments.
Compound Interest: Compound interest is the interest earned on interest. It occurs when the interest earned on an initial principal amount is added back to the principal, and the subsequent interest is calculated on the new, higher balance. This compounding effect allows the total value to grow exponentially over time.
Simple Interest: Simple interest is a method of calculating the amount of interest earned or paid on a principal amount over a specific period of time. It is a straightforward calculation that does not take into account compounding effects.
Principal: The principal is the original amount of money invested or borrowed, upon which interest is calculated. It is the fundamental sum that forms the basis for financial transactions, such as loans, investments, and savings accounts.
I = Prt: I = Prt is a formula used to calculate simple interest, where I represents the total interest earned, P is the principal or initial amount invested, r is the annual interest rate, and t is the time period in years. This formula is a fundamental concept in the context of solving simple interest applications.
Time Period: The time period refers to the duration or span of time over which a particular event, process, or calculation is measured or considered. It is a fundamental concept in various fields, including mathematics, finance, and scientific analysis, where understanding the relevant time frame is crucial for accurate interpretation and decision-making.
Annual Interest Rate: The annual interest rate is the interest rate charged on a loan or paid on an investment over the course of a year. It represents the cost of borrowing money or the return on an investment expressed as a percentage of the principal amount.
Annual Percentage Yield: The annual percentage yield (APY) is a measure of the rate of return on an investment or savings account, taking into account the effect of compounding interest. It represents the total amount of interest an account will earn over a one-year period, expressed as a percentage of the initial balance.
APY: APY, or Annual Percentage Yield, is a metric used to measure the effective annual rate of return on an investment or savings account, taking into account the effect of compounding interest over time. It provides a more accurate representation of the true earning potential of a financial product compared to the stated interest rate alone.
Annual Percentage Rate: The annual percentage rate (APR) is the annual cost of borrowing money, expressed as a percentage rate. It represents the true cost of a loan or credit, including all applicable fees and interest charges, to provide a more accurate representation of the cost compared to just the stated interest rate.
APR: APR, or Annual Percentage Rate, is a measure of the cost of credit expressed as a yearly rate. It is a standardized way of calculating the interest rate on loans, credit cards, and other forms of financing, allowing consumers to compare the true cost of borrowing across different financial products.
CDs: CDs, or Certificates of Deposit, are a type of savings account offered by banks and credit unions that provide a fixed interest rate in exchange for the customer agreeing to keep their money deposited for a specific period of time. CDs are commonly used as a low-risk investment option to earn a higher return than a traditional savings account.
Interest-Only Loans: An interest-only loan is a type of loan where the borrower is only required to pay the interest on the loan for a set period of time, rather than the principal and interest. This allows for lower monthly payments during the interest-only period, but can lead to higher overall costs over the life of the loan.
Savings Accounts: A savings account is a type of bank account that allows individuals to deposit money and earn interest on the balance. It is primarily used for storing and accumulating funds for future financial goals or emergencies, rather than for frequent transactions like a checking account.
Rule of 72: The Rule of 72 is a simple mathematical rule used to estimate the time required for a given investment or account to double in value at a certain interest rate. It provides a quick and easy way to calculate the approximate doubling time of an investment or account balance.
Present Value: Present value is the current worth of a future sum of money or stream of cash flows, given a specified rate of return or discount rate. It is a fundamental concept in finance and economics that allows for the comparison and valuation of cash flows occurring at different points in time.
Investment Yield: Investment yield refers to the return on an investment, typically expressed as a percentage of the original investment amount. It represents the income or profit generated by an investment over a specific period of time, and is a crucial metric for evaluating the performance and potential of different investment options.
Certificates of Deposit: Certificates of Deposit (CDs) are a type of savings account offered by banks and credit unions that provide a fixed interest rate for a predetermined period of time. They are a popular investment option for individuals looking to earn a higher return on their savings while maintaining a low-risk profile.
Future Value: Future Value (FV) is the value of an asset or cash at a future date, based on an assumed rate of growth or interest. It is a fundamental concept in finance and investing, used to determine the potential worth of an investment or savings over time.
Amortization: Amortization is the process of gradually paying off a debt or other obligation over time through a series of scheduled payments. It involves the systematic allocation of the cost or value of an asset, such as a loan or a mortgage, over its useful life or repayment period.