discovering finance dr. hassan sharafuddin discovering mathematics week 7 discovering finance mu123

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Discovering Finance Dr. Hassan Sharafuddin Interest is money. And if you’re the borrower, you pay for the privilege of using the money. If you’re the lender, you’re paid the interest for your service of providing the money. The amount of money being borrowed or loaned is the principal, or the initial amount. The rate of interest is the percentage of the principal that it costs to borrow the money (or that you’re paid for using the money). And the time is the period — in years, months, or days —that the transaction is taking place. The Simple Interest Formula

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Discovering Finance Dr. Hassan Sharafuddin Discovering Mathematics Week 7 Discovering Finance MU123 Discovering Finance Dr. Hassan Sharafuddin Learning Outcomes This unit includes the following sections: -Solving for different values using the simple interest formula. (30 minutes) -Calculating Present value (30 minutes) -Solving Quiz 2 (30 minutes) -Discuss solutions (20 minutes) Week 7 Discovering Finance Dr. Hassan Sharafuddin Interest is money. And if youre the borrower, you pay for the privilege of using the money. If youre the lender, youre paid the interest for your service of providing the money. The amount of money being borrowed or loaned is the principal, or the initial amount. The rate of interest is the percentage of the principal that it costs to borrow the money (or that youre paid for using the money). And the time is the period in years, months, or days that the transaction is taking place. The Simple Interest Formula Discovering Finance Dr. Hassan Sharafuddin The Simple Interest Formula Find simple interest using the simple interest formula I = P x R x T Discovering Finance Dr. Hassan Sharafuddin HOW TO: Identify the principal, rate and time The Simple Interest Formula The price paid for using money is called interest. Principal is the amount borrowed or invested. Rate is the percent of the principal paid as interest per period, usually one year. Time must be expressed in the same unit of time as the rate. (i.e. one year) Discovering Finance Dr. Hassan Sharafuddin The interest formula shows how interest, principal, rate, and time are related and gives us a way of finding one of these values if the other three values are known. Interest = principal * rate * time I = P * R * T I = PRT If the rate is a percent per year, the time must be expressed in years or a decimal or fractional part of a year. Similarly, if the rate is a percent per month, the time must be expressed in months. The Simple Interest Formula Discovering Finance Dr. Hassan Sharafuddin Interest An amount paid or earned for the use of money. Simple interest Interest earned when a loan or investment is repaid in a lump sum. Principal The amount of money borrowed or invested. MORE Key Terms The Simple Interest Formula Discovering Finance Dr. Hassan Sharafuddin Rate The percent of the principal paid as interest per time period. Time The number of days, months or years that the money is borrowed or invested. Key Terms The Simple Interest Formula Discovering Finance Dr. Hassan Sharafuddin Principal = (P) = $1,200 Interest rate = 8% (or 0.08) Time = 1 year Interest = P x R x T Interest = 1,200 x 0.08 x 1 Interest = $96 The interest on the loan is $96 Find the interest paid on a loan The Simple Interest Formula HOW TO: Discovering Finance Dr. Hassan Sharafuddin Simple interest is frequently used when small businesses act as lenders in order to sell products and arrange for payments over the next two years rather than at the end of the time period. For example: Amal purchases a new car from a local dealer. She makes arrangements with the dealer to pay for the $23,995 car over the next 4 years at 5% interest (simple interest). If she is to make equal monthly payments, how much are those payments? The Simple Interest Formula Discovering Finance Dr. Hassan Sharafuddin The Simple Interest Formula Discovering Finance Dr. Hassan Sharafuddin Find the Principal, Rate or Time Using the Simple Interest Formula The I=PRT formula allows you to solve for more than just the amount of interest accumulated. You also can use the formula to find the value of any of the variables if you have the other three. For instance, you can determine the interest rate from the amount of interest paid. Example: Shafi agreed to make quarterly payments of $ for 4 years on a loan of $10,000. What simple interest rate is he paying? Discovering Finance Dr. Hassan Sharafuddin You first need to determine the total amount of money being repaid. If Shafi is making 4 payments a year for 4 years, you know that hes making 16 payments of $ So his total repayment is 16 $ = $12,500. You also know that he borrowed $10,000, so the interest hes paying is: $12,500 $10,000 = $2,500. The interest amount, $2,500, is the answer to the interest formula, I = PRT. So replace the I with $2,500, replace P with $10,000, replace T with 4, and then solve for R. Find the Principal, Rate or Time Using the Simple Interest Formula Discovering Finance Dr. Hassan Sharafuddin Find the Principal, Rate or Time Using the Simple Interest Formula Discovering Finance Dr. Hassan Sharafuddin Find the interest on a 2-year loan of $4,000 at a 6% rate. $480 Find the interest earned on a 3-year investment of $5,000 at 4.5% interest. $675 Examples The Simple Interest FormulaSection 11-1 Discovering Finance Dr. Hassan Sharafuddin Home Assignment Discovering Finance Dr. Hassan Sharafuddin The Simple Interest Formula Find the maturity value of a loan Maturity value is the total amount of money due by the end of a loan period. The amount of the loan and interest. If principal and interest are known, add them. MV = principal + PRT MV = P(1+RT) Discovering Finance Dr. Hassan Sharafuddin Marcus Logan can purchase furniture on a 2-year simple interest loan at 9% interest per year. What is the maturity value for a $2,500 loan? MV = P(1 + RT); (substitute known values) MV = $2,500 ( x 2) MV = $2,500 ( ) MV = $2,500 (1.18) MV = $2,950 Marcus will pay $2,950 at the end of two years. An Example The Simple Interest Formula Discovering Finance Dr. Hassan Sharafuddin Amjad is going to borrow $4,000 at 7.5% interest. What is the maturity value of the loan after three years? $4,900 Hanan will invest $3,000 at 8% for 5 years. What is the maturity value of the investment? $4,200 Examples The Simple Interest Formula Discovering Finance Dr. Hassan Sharafuddin Calculating Present Value The simple interest method is restricted primarily to loans and investments having terms of less than one year. The compound interest method is employed in cases where the term exceeds one year. In the compound interest method, interest is periodically calculated and converted to principle. It means that interest is added to the principle and is thereafter treated as principal. Discovering Finance Dr. Hassan Sharafuddin Calculating Present Value Example: Susan secured a small business loan of $8000 for three years, compounded annually. If the interest rate was 9%, find the future value (compound amount). Solution: There are three interest periods, one for each of the three years. First year = (8000 x 0.09 X 1) = = 8720 (this is maturity for year 1) Second year = (8720 X 0.09 X 1) = = (MV for year 2) Third year = X 0.09 X 1) = = (MV for year 3) The future value is $10,360.23 Discovering Finance Dr. Hassan Sharafuddin Calculating Present Value Discovering Finance Dr. Hassan Sharafuddin Exercise: A loan of $2,950 at 8% is made for two years compounded annually. Find the future value (compound amount) of the loan. Find the amount of interest paid on the loan. Answer: The future value = $3, The compound interest = $ Calculating Present Value Discovering Finance Dr. Hassan Sharafuddin Calculating Present Value Discovering Finance Dr. Hassan Sharafuddin Exercise: Compute the amount of money to be set aside today to ensure a future value of $2,500 in one year if the interest rate is 2.5% annually, compounded annually. Answer: $ (to 2 d.p.) Calculating Present Value Discovering Finance Dr. Hassan Sharafuddin Solve Quiz 2 (30 minutes) Discuss solutions (20 minutes)