Compound Interest PDF

Topic... Compound Interest SLIDESMANIA.COM  Objectives 1. Illustrates compound interest 2. Computes interest and present value in compound interest 3. Solv...

Topic... Compound Interest SLIDESMANIA.COM  Objectives 1. Illustrates compound interest 2. Computes interest and present value in compound interest 3. Solve word problems involving compound interest SLIDESMANIA.COM  DEFINITION Compound interest is the interest added to the principal of an investment or a loan so that the added interest also earns interest from then on. This addition of interest to the principal is called compounding. SLIDESMANIA.COM  TERMS related to Compound Interest TERM DEFINITION Conversion Period Time interval between succeeding Compounding Period interest calculations Interval Period Compound Frequency Number of compounding that takes Conversion Frequency place in a year SLIDESMANIA.COM  TERMS related to Compound Interest TERM DEFINITION Annual interest rate on which the Nominal Interest compound interest calculation is based Periodic Interest Rate of interest earned in one Rate conversion period SLIDESMANIA.COM  Compounding Frequencies and Periods Compounding or Number of compounding conversion frequency or conversions per year Annually 1 Semi-annually 2 Quarterly 4 Bimonthly 6 SLIDESMANIA.COM Monthly 12 01 SLIDESMANIA.COM  𝐦𝐭 𝐣 FORMULA: 𝐌𝐕 = 𝐏𝐕 𝟏 + = 𝐏𝐕 𝟏 + 𝐢 𝐧 𝐦 𝐣 Where: 𝐢= 𝐧 = 𝐦𝐭 𝐦 MV = Maturity Value PV = Present Value (Principal) j = nominal interest rate per year (Annual rate) m = number of conversion periods per year i = rate per conversion period n = total number of conversion periods t = term (number of years)  𝐦𝐭 𝐣 FORMULA: 𝐌𝐕 = 𝐏𝐕 𝟏 + = 𝐏𝐕 𝟏 + 𝐢 𝐧 𝐦 𝐣 Where: 𝐢= 𝐧 = 𝐦𝐭 𝐦 FORMULA in solving PV: 𝐌𝐕 𝐏𝐕 = 𝐧 𝟏+𝐢  Complete the table. Nominal Number of Maturity Value Conversion term Interest Present Compound Interest compounding (MV) Period (m) (t) Rate (i) Value (PV) Interest (CI) Rate (j) periods (n) 𝟎. 𝟎𝟑 1. P5,000.00 3% quarterly 2 years 𝟒 8 P4,709.87 P290.13 𝟎. 𝟎𝟓𝟒 2. P8,924.25 5.4% semi-annually 1 year 𝟐 2 P8,461.41 P462.84 5 years 𝟎. 𝟐𝟑 3. P12,010.00 23% annually 2 months 𝟏 5.17 P4,118.51 P7,891.49 3 years 𝟎. 𝟎𝟗𝟐𝟏 4. P28,980.50 9.21% monthly 6 months 𝟏𝟐 42 P21,020.16 P7,960.34 SLIDESMANIA.COM  Solution #1 Given: MV = ₱5,000.00; j = 3% = 0.03; m = quarterly = 4 t = 2 years SLIDESMANIA.COM  Solution #1 Solve for the interest rate (i) j 0.03 i= = m 4 Solve for the no. of compounding periods (n) n = mt = 4 2 = 8 SLIDESMANIA.COM  Solution #1 Given: MV = ₱5,000.00; 0.03 i= 4 n=8 Unknown: Present Value (PV) MV PV = 1+i n 5000 5000 PV = 8 = 0.03 1.0616 1+ SLIDESMANIA.COM 4 𝐏𝐕 = 𝐏𝟒, 𝟕𝟎𝟗. 𝟖𝟕  Solution #1 Unknown: Compound Interest (CI) MV = P5,000.00 PV = P4,709.87 CI = MV − PV CI = P5,000.00 − P4,709.87 𝐂𝐈 = 𝐏𝟐𝟗𝟎. 𝟏𝟑 SLIDESMANIA.COM  Solution #2 Given: MV = ₱8,924.25; j = 5.4% = 0.054; m = semi-annually = 2 t = 1 year SLIDESMANIA.COM  Solution #2 Solve for the interest rate (i) j 0.054 i= = m 2 Solve for the no. of compounding periods (n) n = mt = 2 1 = 2 SLIDESMANIA.COM  Solution #2 Given: MV = ₱8,924.25; 0.054 i= 2 n=2 Unknown: Present Value (PV) MV PV = 1+i n 8924.25 8924.25 PV = = 0.054 2 1.0547 1+ SLIDESMANIA.COM 2 𝐏𝐕 = 𝐏𝟖, 𝟒𝟔𝟏. 𝟒𝟏  Solution #2 Unknown: Compound Interest (CI) MV = P8,924.25 PV = P8,461.41 CI = MV − PV CI = P8,924.25 − P8,461.41 𝐂𝐈 = 𝐏𝟒𝟔𝟐. 𝟖𝟒 SLIDESMANIA.COM  Solution #3 Given: MV = ₱12,010.00; j = 23% = 0.23; m = annually = 1 2 t = 5 years and 2 months = 5 = 5.17 12 SLIDESMANIA.COM  Solution #3 Solve for the interest rate (i) j 0.23 i= = m 1 Solve for the no. of compounding periods (n) n = mt = 1 5.17 = 5.17 SLIDESMANIA.COM  Solution #3 Given: MV = ₱12,010.00; 0.23 i= 1 n = 5.17 Unknown: Present Value (PV) MV PV = 1+i n 12010 12010 PV = 5.17 = 0.23 2.9161 1+ SLIDESMANIA.COM 1 𝐏𝐕 = 𝐏𝟒, 𝟏𝟏𝟖. 𝟓𝟏  Solution #3 Unknown: Compound Interest (CI) MV = P12,010.00 PV = P4,118.51 CI = MV − PV CI = P12,010.00 − P4,118.51 𝐂𝐈 = 𝐏𝟕, 𝟖𝟗𝟏. 𝟒𝟗 SLIDESMANIA.COM  Solution #4 Given: MV = ₱28,980.50; j = 9.21% = 0.0921; m = monthly = 12 6 t = 3 years and 6 months = 3 = 3.5 12 SLIDESMANIA.COM  Solution #4 Solve for the interest rate (i) j 0.0921 i= = m 12 Solve for the no. of compounding periods (n) n = mt = 12 3.5 = 42 SLIDESMANIA.COM  Solution #4 Given: MV = ₱28,980.50; 0.0921 i= 12 n = 42 Unknown: Present Value (PV) MV PV = 1+i n 28980.50 28980.50 PV = 42 = 0.0921 1.3787 1+ SLIDESMANIA.COM 12 𝐏𝐕 = 𝐏𝟐𝟏, 𝟎𝟐𝟎. 𝟏𝟔  Solution #4 Unknown: Compound Interest (CI) MV = P28,980.50 PV = P21,020.16 CI = MV − PV CI = P28,980.50 − P21,020.16 𝐂𝐈 = 𝐏𝟕, 𝟗𝟔𝟎. 𝟑𝟒 SLIDESMANIA.COM 02 SLIDESMANIA.COM  Sample Problem 1 What amount must Mr. John Soriano invest now in a savings account earning 6% compounded quarterly to accumulate a total of P25,000.00 after 4 years? SLIDESMANIA.COM  Solution Given: MV = ₱25,000.00; j = 6% = 0.06; m = quarterly = 4 t = 4 years SLIDESMANIA.COM  Solution Solve for the interest rate (i) j 0.06 i= = m 4 Solve for the no. of compounding periods (n) n = mt = 4 4 = 16 SLIDESMANIA.COM  Solution Given: MV = ₱25,000.00; 0.06 i= 4 n = 16 Unknown: Present Value (PV) MV PV = 1+i n 25000 25000 PV = 16 = 0.06 1.2690 1+ SLIDESMANIA.COM 4 𝐏𝐕 = 𝐏𝟏𝟗, 𝟕𝟎𝟎. 𝟓𝟓  Sample Problem 2 Ms. Carla Oliveros has just been notified that the combined principal and the interest on an amount that she borrowed 30 months ago at 14% compounded semi-annually, is now P75,160.00. How much of this amount is the principal? SLIDESMANIA.COM  Solution Given: MV = ₱75,160.00; j = 14% = 0.14; m = semi-annually = 2 30 t = 30 months = = 2.5 12 SLIDESMANIA.COM  Solution Solve for the interest rate (i) j 0.14 i= = m 2 Solve for the no. of compounding periods (n) n = mt = 2 2.5 = 5 SLIDESMANIA.COM  Solution Given: MV = ₱75,160.00; 0.14 i= 2 n=5 Unknown: Present Value (PV) MV PV = 1+i n 75160 75160 PV = = 0.14 5 1.4026 1+ SLIDESMANIA.COM 2 𝐏𝐕 = 𝐏𝟓𝟑, 𝟓𝟖𝟔. 𝟐𝟎  Sample Problem 3 Ms. Sofia Traje paid P88,600.00 on a loan made 2 years before at 11.2% compounded bi-monthly. How much of this amount is the principal? SLIDESMANIA.COM  Solution Given: MV = ₱88,600.00; j = 11.2% = 0.112; m = bi-monthly = 6 t = 2 years SLIDESMANIA.COM  Solution Solve for the interest rate (i) j 0.112 i= = m 6 Solve for the no. of compounding periods (n) n = mt = 6 2 = 12 SLIDESMANIA.COM  Solution Given: MV = ₱88,600.00; 0.112 i= 6 n = 12 Unknown: Present Value (PV) MV PV = 1+i n 88600 88600 PV = 12 = 0.112 1.2485 1+ SLIDESMANIA.COM 6 𝐏𝐕 = 𝐏𝟕𝟎, 𝟗𝟔𝟓. 𝟏𝟔