How to Find the Total Amount Paid in an Interest Rate Equation (2024)

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1Understanding Interest Rate Equations

2Solving an Interest Rate Equation to Find the Total Amount Paid

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Reviewed byAlex Kwan

Last Updated: December 17, 2023

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If you have been given a math problem that requires you to find the total amount of money paid over a certain period of time, don’t worry. These equations are simple to solve if you understand what the parts of the equation are and how to use them.

Method 1

Method 1 of 2:

Understanding Interest Rate Equations

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  1. 1

    Understand the terms you will be working with in your interest rate equation. When you are solving an interest rate equation, such as that for an interest rate you have for a loan you took out, you will work with several different variables. These include:

    • P = principal amount borrowed.
    • i = the interest rate.
    • N = the term of the loan, in years.
    • F = the total amount paid at the end of the designated number of years.
  2. 2

    Know the equation used to calculate the total amount you will pay. To find the total amount paid at the end of the number of years you pay back your loan for, you will have to multiply the principal amount borrowed with 1 plus the interest rate. Then, raise that sum to the power of the number of years. The equation looks like this:

    • F = P(1 + i)^N

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  3. 3

    Read through the equation you are given and determine which numbers coincide with each variable of the equation. Normally, interest rate problems will be given in sentence format and you will have to figure out what each number represents. For example, you are given: “You borrow $4,000 from a bank and promise to repay the loan principal plus the accumulated interest in four years at a rate of 10% per year. How much would you repay at the end of 4 years?”.

    • P would be $4,000.
    • i would be 10%.
    • N would be 4 years.
    • F would be what you are trying to find.
  4. 4

    Plug the known numbers into the equation for fixed rate. Once you have figured out what numbers you are working with, you can plug the numbers in so that you can work with the equation to find the fixed rate. Our equation would be:

    • F = 4000(1 + 10%)^4. Note that to make things easier, you can convert the interest percentage to decimals so the equation would be F = 4000(1 + 0.1)^4
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Method 2

Method 2 of 2:

Solving an Interest Rate Equation to Find the Total Amount Paid

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  1. 1

    Work through the problem in stages. In order to find the total amount you will pay over the course of the time you pay back a loan, you will have to work through the article in stages. Let’s look at an example article:

    • ”You borrow 5,000 from a bank and plan to repay the loan principal, plus and accumulated interest in five years. The rate of the interest is 10%. How much will you pay, in total, at the end of the five years?
  2. 2

    Create your equation. Once you have read through the article, create an equation based on the standard equation F = P(1 + i)^N. For our question, our equation would be:

    • F = 5000(1 + 0.1)^5.
  3. 3

    Solve the inside of the parentheses first. When you have written out your equation, start to solve your problem. The first step towards doing this is to solve the equation within the parentheses first. For our equation:

    • Solve (1 + 0.1) = 1.1. So now our equation looks like this: F = 5000(1.1)^5.
  4. 4

    Use N to solve the next part of the equation. Once you have simplified the information in the parentheses, you should move onto applying the years (N) of the equation. This means raising the number inside the parentheses to the Nth degree. For our equation:

    • (1.1)^5 means multiplying 1.1 to itself five times. In this case, (1.1)^5 = 1.61051.
  5. 5

    Finish the equation. You should now only have one step left in the process of solving your equation. To finish the equation and find F, or the total amount paid, you will have to multiply P with the number in the parentheses. For our equation:

    • F = 5000(1.61051) therefore, F = $8,052.55. That means that you would have paid $8,052.55 over the course of the five years.
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      About This Article

      How to Find the Total Amount Paid in an Interest Rate Equation (29)

      Reviewed by:

      Alex Kwan

      Certified Public Accountant

      This article was reviewed by Alex Kwan. Alex Kwan is a Certified Public Accountant (CPA) and the CEO of Flex Tax and Consulting Group in the San Francisco Bay Area. He has also served as a Vice President for one of the top five Private Equity Firms. With over a decade of experience practicing public accounting, he specializes in client-centered accounting and consulting, R&D tax services, and the small business sector. This article has been viewed 150,470 times.

      58 votes - 51%

      Co-authors: 5

      Updated: December 17, 2023

      Views:150,470

      Categories: Finance and Business

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      How to Find the Total Amount Paid in an Interest Rate Equation (2024)

      FAQs

      How to Find the Total Amount Paid in an Interest Rate Equation? ›

      To find the total amount paid at the end of the number of years you pay back your loan for, you will have to multiply the principal amount borrowed with 1 plus the interest rate. Then, raise that sum to the power of the number of years. The equation looks like this: F = P(1 + i)^N.

      How to calculate total amount paid with interest? ›

      Total amount paid with interest is calculated by multiplying the monthly payment by total months. Total interest paid is calculated by subtracting the loan amount from the total amount paid. This calculation is accurate but not exact to the penny since, in reality, some actual payments may vary by a few cents.

      What is the formula for amount of interest paid? ›

      The simple interest expense formula is Interest Expense = Principal x Rate x Time. r = The rate of interest expressed as a decimal.

      What is the formula for total amount? ›

      Amount (A) = Principal (P) + Interest (I)

      Where, Amount (A) is the total money paid back at the end of the time period for which it was borrowed.

      How do you calculate how much interest has been paid? ›

      Step 1: Convert your annual interest rate to a monthly rate by dividing by 12. Step 2: Multiply your loan amount by your monthly interest rate to get your monthly interest payment. Step 3:To calculate your monthly principal payment, subtract your monthly interest payment from your total monthly payment.

      How to find total amount in simple interest? ›

      If you'd like to calculate a total value for principal and interest that will accrue over a particular period of time, use this slightly more involved simple interest formula: A = P(1 + rt). A = total accrued, P = the principal amount of money (e.g., to be invested), r = interest rate per period, t = number of periods.

      What is the formula for calculating interest amount? ›

      To calculate interest rates, use the formula: Interest = Principal × Rate × Tenure. This equation helps determine the interest rate on investments or loans. How do you calculate borrowed interest? Calculate borrowed interest using the formula: Interest = Principal * Rate * Time.

      How do you calculate real interest paid? ›

      To calculate a real interest rate, you subtract the inflation rate from the nominal interest rate. In mathematical terms we would phrase it this way: The real interest rate equals the nominal interest rate minus the inflation rate.

      How do you calculate total money after interest? ›

      Use this simple interest calculator to find A, the Final Investment Value, using the simple interest formula: A = P(1 + rt) where P is the Principal amount of money to be invested at an Interest Rate R% per period for t Number of Time Periods. Where r is in decimal form; r=R/100; r and t are in the same units of time.

      What is total amount paid? ›

      Total amount paid means the total amount paid by the consumer in relation to a payment protection contract, including any Insurance Premium Tax payable.

      What does total interest paid mean? ›

      The total interest percentage is calculated by adding up all of the scheduled interest payments, then dividing the total by the loan amount to get a percentage. The calculation assumes that you will make all your payments as scheduled. The calculation also assumes that you will keep the loan for the entire loan term.

      What is the formula for simple interest rate? ›

      Interest formula for simple interest: I = Prt where I is the total amount of interest accrued; over t time periods at a simple interest rate, r, and where the original amount invested or borrowed is P.

      What is the formula for total interest paid? ›

      To start, you'd multiply your principal by your annual interest rate, or $10,000 × 0.05 = $500. Then, you'd multiply this value by the number of years on the loan, or $500 × 5 = $2,500. Now that you know your total interest, you can use this value to determine your total loan repayment required.

      How is interest calculated and paid? ›

      The formula for calculating simple interest is: Interest = P * R * T. P = Principal amount (the beginning balance). R = Interest rate (usually per year, expressed as a decimal). T = Number of time periods (generally one-year time periods).

      How to calculate a rate? ›

      To find a rate in math, divide the value of the dependent variable by the value of the independent variable. Then, reduce the fraction if possible.

      What is 6% interest on a $30,000 loan? ›

      For example, the interest on a $30,000, 36-month loan at 6% is $2,856.

      How to calculate total loan amount with interest rate? ›

      A = P (1 + r/n) ^ nt
      1. A = Total Amount Paid.
      2. P = Principal Amount.
      3. R = Rate of Interest.
      4. N = number of times interest is compounded per year.
      5. T = Number of years.

      How do you calculate total repayment including interest? ›

      How to Calculate Monthly Loan Payments
      1. If your rate is 5.5%, divide 0.055 by 12 to calculate your monthly interest rate. ...
      2. Calculate the repayment term in months. ...
      3. Calculate the interest over the life of the loan. ...
      4. Divide the loan amount by the interest over the life of the loan to calculate your monthly payment.

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