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Understanding Simple and Compound Interest in Business Math

Learn how to calculate simple and compound interest for business investments, loans, and savings. Includes examples and formulas for easy understanding and application.

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Understanding Simple and Compound Interest in Business Math

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  1. Business Math2 Revision

  2. Example Christina Jones paid the bank $44 interest at 11% for 120 days. How much did she borrow? Principal = Interest Rate x Time $44 . P = .11 x (120/360) = $1,200

  3. Example Christina Jones borrowed $1,200 from the bank. Her interest is $44 for 120 days. What rate of interest did Christina pay? $44 . R = $1,200 x (120/360) = .11

  4. Example Christina Jones borrowed $1,200 from the bank. Her interest is $44 for 11%. How much time does Christina have to repay the loan? $44 . T = $1,200 x .11 = .33 .33 x 360 = 120 days

  5. Simple interest

  6. Example Let's say you decided to start a candle-making business for some extra income. You already had several orders, but because you let customers pay once they got their candles, you needed $2,000 startup money to purchase supplies and equipment. You borrowed the $2,000 for two years at a simple interest rate of 10%. At the end of the two years, how much interest would be paid? If you sold the candles for $6.00 each, how many candles (sold) would cover the interest?

  7. Simple interest

  8. Examples • What is the interest rate for the investment of a person who deposits 500$ in a bank for 5 months and 600$ for 8 months and 700$ for 12 months knowing that the total maturity value =2000$

  9. Examples • A person invested a principal P in bank A for 5 months, the bank offers an interest rate of 10%, and invested the same amount in bank B that offers a rate of 8% for 7 months • If the man had a total amount of 3000$ at the end of the periods, what was P?

  10. Examples • Ahmad borrowed 500$ from a bank in April 3, when the loan matured, he repaid 530$. If you know that the interest rate in this bank was 8%, at what day Ahmad repaid the loan?

  11. Examples • Ali borrowed 20,000$ from a bank for 219 days, If the difference between the exact interest and the ordinary interest at the end of the period was 10$, What was the interest rate in that bank?

  12. Examples • Omar invested a principal P in bank A for a year. The interest was 50$ at the end of the year. He invested the same amount in bank B which its interest rate increases 1% than the first bank. The interest in the second bank was 165$ after 3 years. What was P and the interest rate in the two banks?

  13. Examples • A person borrowed three loans • 1000$ in 25 March 1980 • 2000$ in 17 June 1980 • 3000$ in 28 August 1980 • In 30 November 1980 the bank informed him that the total maturity in that date is 6216$. What was the interest rate in that bank

  14. Example • find the future value and compound interest on $2,000 invested for four years compounded semiannually at 8%. • FV = $2,737.14 • CI = $737.14 • What would the simple interest be for the same loan? • $640

  15. Examples compound interest • Calculate the amount of money needed now to purchase a laptop computer and accessories valued at $2,000 in a year if you invest the money at 6%. • $1,886.79 • John wants to replace a tool valued at $150 in a year. How much money will he have to put into a savings account that pays 3% annual interest? • $145.63

  16. Examples • How much money would you have to invest for 5 years at 6% paid semi-annually to make a down payment of $20,000 on a house? • $14,881.80 • How much money would you have to invest for 3 years at 10% paid semi-annually to purchase an automobile that costs $20,000? • $14,924.40

  17. Uniform Payment Series Sum of interest = Where A : the payment at the end (or start) of the period N: number of payments

  18. Uniform Payment Series Value of payments (Future value)= sum of payments + sum of interests Future value of payments =

  19. Examples A person deposits 100$ in a bank at the end of the month for 2 years. Find the future value of these payments at the end of the years if you know that interest rate is 10% Period of the first payment= 23 months Period of the last payment= 0 A = 100$ n= 24 payments R = 10 % yearly

  20. Future value of payments = 12

  21. Examples A person deposits 300$ in a bank every 3 months for one year. Find the future value of these payments at the end of the year if you know that interest rate is 6% Two solutions: If the payments paid at the start of the three months If the payments paid at the end of the three months

  22. Solution 1 If the payments paid at the start of the three months Period of the first payment= 12 months Period of the last payment= 3 months A = 300$ n= 4 payments R = 6 % yearly

  23. Solution 2 If the payments paid at the end of the three months Period of the first payment= 9 months Period of the last payment= 0 A = 300$ n= 4 payments R = 6 % yearly

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