Applied Mathematics of Investment - Simple Interest

Applied Mathematics of Investment First semester 2024-2025 LESSON 1: SIMPLE INTEREST Learning Objective: At the end of this lesson, you must have: ▪ Solved real-life problems involving simple interest on loans and investments. Let’s Learn! To better pre...

Applied Mathematics of Investment First semester 2024-2025 LESSON 1: SIMPLE INTEREST Learning Objective: At the end of this lesson, you must have: ▪ Solved real-life problems involving simple interest on loans and investments. Let’s Learn! To better prepare yourself from the lesson ahead, answer the short activity below. The following are in percentage form. Convert each into decimal. 1) 5% = 2) 25% = 3) 1% = 4) 100% = 5) 3% = The conversion from percentage to decimal is an important knowledge for you to be able to compute for interest, both simple and compound. Interest plays an important part in our lives. Understanding interest is an important skill in life. When you learn to calculate simple and compound interest, it can help you make wise and informed financial decisions in the future. Computing interest is a must in evaluating loan and investment proposals. Interest can be calculated in different ways using different methods. There are two types of interests: Simple Interest and Compound Interest. 1.1 Nature of Interest Interest may be described as the fee for using the borrowed money. It is an expense for the person who borrows money and income for the person who lends money. Interest is charged at a certain rate on the principal amount for a given period. It refers to the amount received because of the possession or ownership of a contractual obligation to pay on the part of another. Interest also serves as a mechanism of Applied Mathematics of Investment First semester 2024-2025 imposing penalty to a borrower for not paying a matured financial obligation at a specified time. Interest emanates from certain transactions which are economic or financial in character. 1.2 Parties Involved in the Payment of Interest: Lender or creditor - Refers to the party lending money or extending credit. - He/she expects to earn income from this transaction. Borrower or debtor - Refers to the party using the money or credit. - He/she expects future expenses as the cost of using it. 1.3 Elements of Interest Computation Principal - Refers to the amount of money extended for credit, or the money deposited in the bank for safekeeping. Interest Rate - Refers to the charged amount for using the money over a certain period. It is expressed in percent per year unless indicated otherwise in the problem. expressed in percent per year unless otherwise indicated in the problem. TIME - Refers to the period covered from the time that the money (principal) is borrowed until its due date. The due date for the payment of the principal is known as the maturity date. ***Illustration 1.1 On March 1, 2019, Ms. Jo borrowed Php1,000,000.00 from Metro Savings at 10% interest, payable on March 1, 2020, to finance the construction of her manufacturing plant. Based on the data: Principal = PHP 10,000,000.00 Interest Rate = 10% Time = 1 Year (March 1, 2019 – March 1, 2020) 1.4 Simple Interest Applied Mathematics of Investment First semester 2024-2025 Simple interest is the interest paid only on the PRINCIPAL and not on any accumulated interest. It is an interest that is computed only once from the time the amount is borrowed until it is paid. Under the concept of simple interest, the amount of interest is usually paid at the maturity date of due date. The formula to compute the simple interest is as follows: Interest = Principal x Rate x Time Or I=PRT where: I = Interest P = Principal R = Rate T = Time ***Illustration 1.2 Alexa borrowed Php600,000 from ABC Lending on March 1, 2019, at 9 percent interest, which is payable after 1 year. Find the simple interest. Given: P = 600,000.00 R = 9% or.09 T = 1 year Solution: I=? I=PRT I = (600,000.00) (9%) (1year) I = 54,000.00 ***Illustration 1.3 On June 1, 2019, James borrowed a sum of money from Land City Bank, payable for 3 years at 6% simple interest. She paid Php 9,900 for the interest of her loan. Find how much was borrowed by James. Given: P =? R = 6% or.06 T = 3 years I = 9,900.00LEARNING MODULE IN APPLIED MATHEMATICS OF INVESTMENT Applied Mathematics of Investment First semester 2024-2025 Solution: I=PRT P = I/RT P = 9,900.00/(6%) (3years) P = 55,000.00 ***Illustration 1.4 Jenny borrowed 90,000 from Phil Bank at 9% simple interest. She paid 16,200 as interest upon payment of the principal on the maturity date. Determine how long it took her to pay the money in full. Given: P = 90,000.00 R = 9% or.09 T =? I = 16,200.00 Solution: I=PRT T = I/PR T = 16,200.00/(90,000.00)(9%) = 2 years ***Illustration 1.5 Suppose Alex borrowed 10,000 from a certain lending institution to pay her daughter’s tuition with 2% interest rate per month for 2 months. (a) How much is the simple interest for two months? (b) How much is the total amount to pay including the principal amount and interest to the lender? Problem (a): How much is the simple interest for 2 months? Given: P = 10,000 R = 2% or.02 T = 2 months Applied Mathematics of Investment First semester 2024-2025 I =? Solution: I=PRT I = (10,000) (.02) (2 months) I = Php 400.00VESTMEN Problem (b): How much is the total amount to pay including the principal amount and interest to the lender for two months? Given: P = 10, 000 I = 400.00 Total amount = ? Solution: Total amount = P + I Total amount = 10,000 + 400 Total amount = Php 10, 400