Module 12 Simple and Compound Interest PDF

MODULE 12: SIMPLE AND COMPOUND INTEREST TARGET SKILLS After going through the module, you are expected to:  illustrates simple and compound interests.  distinguishes between simple and compound interests.  computes...

MODULE 12: SIMPLE AND COMPOUND INTEREST TARGET SKILLS After going through the module, you are expected to:  illustrates simple and compound interests.  distinguishes between simple and compound interests.  computes interest, maturity value, future value, and present value in simple interest and compound interest environment.  solves problems involving simple and compound interests. REVIEW DISCUSSION BOARD. Your mother cooks delicious leche flan. You decided to sell your mother’s leche flan online since she lost her job because of the community quarantine during this pandemic. However, you don’t have enough savings to start your online selling. How can you get enough money to start your online selling? BUILD YOUR UNDERSTANDING DISCUSSION BOARD. A. Guide Questions for class discussion 1. Why do you think one needs to make investments? 2. Cite the different investment products banks offered. 3. Enumerate the advantages and disadvantages in choosing the investment offers. 4. What is the ideal investment product that fit your needs? 5. How do banks, credit cooperatives or appliance centers make money from their client? B. Suppose you received ₱10,000 additional commission for selling 5 cars in one quarter. You plan to invest it for 5 years. Option A: ABC Cooperative at 2% per year. Option B: XYZ Bank at 2% compounded annually. The two investment institutions presented the cash flow of your investment. Given: ABC Cooperative P = ₱ 10,000 I = 2% or 0.02 t = 5 years 1|Page  Given: XYZ Bank P = ₱ 10,000 r = 2% or 0.02 t = 5 years m = 1 (compounded annually) Questions: 1. How does the future value is accumulated in simple interest and compound interest? 2. If you are going to invest your money, will you choose those offering simple interest or compound interest? 3. If you are going to lend a money, will you choose lending companies offering simple or compound interest? 2|Page  DEFINITION OF TERMS Note: When the time is expressed in months (m), convert it to years t = 12 Drill: Use your calculator to complete the table below. 3|Page  PROBLEMS INVOLVING SIMPLE INTEREST Solution: Step 1: Identify the given information Problem 1: P = Php19 450 r = 4% = 0.04 Jessa made a loan of P t = 3 years A = ______ 19 450 from a bank that Step 2: Identify what is asked in the problem and the formula to be used. = 1 + charges 4% simple interest. Step 3: Substitute the given values and compute the unknown value. = 1 + = 19 450[1 + 0.04 3 ] = ℎ 21 780 Thus, she must pay Php21 780. How much must she pay the bank after 3 years? 4|Page  Solution: Step 1: I = P1 620 P = Php18 000 r = _______ 6 t = 6 months / 12 = 0.5 years Step 2: = Step 3: 1620 = (18000)(0.5) =. 18 18% Thus, the rate of interest charged to Andrea is 18% Solution: Step 1: I = Php1 050 P = _____ r = 6.5% = 0.065 9 t = 9 months/ 12 = 0.75 years Step 2: = Step 3: 1050 = 0.065 0.75 = 21 538. 46 Thus, she borrowed Php21 538.46 Solution: Step 1: I = Php1 065 P = Php15 800 r = 10.25% =.1025 t = _______ Step 2: = Step 3: 1065 = 15800.1025 ≈ 0.66 0.66 12 = 7.92 ≈ 8 ℎ Thus, her investment will take 8 months to earn an interest of Php1 065 5|Page  Notation Terminology Definition The payment for the use of I Compound Interest borrowed money or the amount earned on invested money P Principal/Present Value The original amount r Nominal Rate Annual interest rate The number of years for which t Time the money is borrowed or invested Final F The accumulated value or Amount/Compounded compound amount Amount Frequency of conversion periods in one year m Conversion Period Annually: m=1 Semianually: m=2 Quarterly: m=4 Monthly: m = 12 i Rate of interest per period = Total number of n n = mt conversion period 6|Page  NOTATION FORMULA I = + − P − = + r = − t = + A = + 7|Page  PROBLEMS INVOLVING COMPOUND INTEREST Solution: Step 1: Identify the given information P = Php47 000 r = 14.74% =.1474 t = 30 years m = quarterly = 4 n = mt = (4)(30) = 120 A = _______ Step 2: dentify what is asked in the problem and the formula to be used. = + Step 3: Substitute the given values and compute the unknown value.. 1474 120 = 47 000 1 + 4 = 3 614 179. 34 He will have Php3 614 179. 33 in his account after 30 years. Solution: Step 1: P = Php125 000 r = 8% = 0.08 t = _______ m = quarterly = 4 A = P176 000 Step 2: = + Step 3: 176 000 log = 125 000 0.08 4 log 1 + 4 = 4.32 ≈ 4 4 ℎ The money was borrowed for 4 years and 4 months 8|Page  Solution: Step 1: P = Php26 900 r = _______ t = 2 years m = monthly = 12 n = (12)(2) = 24 A = 37 850 Step 2: = − Step 3: 1 37 850 24 = 12 −1 26 900 =. 17197 = 17.20% The interest rate is 17.20% Solution: Step 1: P = ______ r = 19% = 0.19 t = 5 years A = Php376 800 m = monthly = 12 n = (12)(5) = 60 Step 2: − = + Step 3: −60 0.19 = 376 800 1 + 12 = 146 812.60 Adamson University should invest Php146 812.60. DISCUSSION BOARD. Compare the graph of compound and simple interest as illustrated below. 9|Page  Reflect Upon As a lender, what do you think is the most reasonable interest you will apply to the money borrowed? REMEMBER Notation Terms Definition Formula The payment for the use of borrowed money I Interest or the amount earned on invested money = P Principal The amount borrowed or invested = A fractional part of the principal that is paid r Rate of interest on loan or investment (%) = The number of years for which the money is t Time/Term borrowed or invested = Final Amount/Maturity The sum of the principal and the interest A Amount earned within the time = + = + Notation Terminology Definition Formula The payment for the use of borrowed I Compound Interest money or the amount earned on invested = + − money − P Principal/Present Value The original amount = + r Nominal Rate Annual interest rate = − The number of years for which the money t Time is borrowed or invested = + Final The accumulated value or compound F Amount/Compounded amount = + Amount 10 | P a g e  Frequency of conversion periods in one Annually: m=1 year Semianually: m = 2 m Conversion Period Quarterly: m=4 Monthly: m = 12 Rate of interest per i period = = Total number of n conversion period n = mt n = mt CHECK YOUR UNDERSTANDING Refer to your e-book. Answer page 139, Firm Up A and 151 Deepen Your Understanding 11 | P a g e