Time Value of Money - Simple & Compound Interest PDF

CHAPTER 2 Time value of money – Simple & Compound Interest: Learning Objectives: Understand the concept of Interest, simple interest and compound interest Apply the concept of interest in various calculations Applying Rule of 72  ACTIVITY 1- 15 mins Considering you got RO 1,000 identi...

CHAPTER 2 Time value of money – Simple & Compound Interest: Learning Objectives: Understand the concept of Interest, simple interest and compound interest Apply the concept of interest in various calculations Applying Rule of 72  ACTIVITY 1- 15 mins Considering you got RO 1,000 identify various options that will allow your money to grow? Time duration: 5 mins to think and write 10 mins class discussion https://shabiba.eu-central-1.linodeobjects.com/2021/02/1612255477-1612255477- u3q2fwf3a84x.jpg  Interest: Monetary Reward or Charge Deposits and Borrowings Provided by Banks & Financial institutions Two types https://www.cimbbank.com.ph/content/dam/cimbph/im ages/financial-literacy/how-to-compute-for-my-money- after-interest/VAF-01.jpg Simple interest Interest is simply calculated on the principal amount of money deposited or borrowed. Formula for simple interest (I) = P x r x t P = Principal amount = refers to the amount deposited into the bank or borrowed from the bank. r = Interest rate = the rate provided or charged by the bank. t = Time period in years = refers to the number of years for which the money is deposited or borrowed from the bank.  Simple interest - Example you have a saving of RO The solution will be: 1,000 in a bank which For 2 years: gives interest @ 4% p.a. 4 What will be the amount P = 1,000 , r = 100 = 0.04%, t = 2 you will be the Interest Interest received = 1,000 x 0.04 x 2 = RO 80 received on such deposit: For 2 years For 15 months: For 15 months 4 P = 1,000 , r = 100 = 0.04%, t = 15 months 15 Interest received = 1,000 x 0.04 x 12 = RO 60  Simple interest – Exercise 1 Find out the amount of interest on a deposit of RO 5,000 for 4 years at the rate of 4% simple interest.  Simple interest – Exercise 2 Calculate the amount of principal if the amount of interest received of a deposit of 5 years is RO 250 at the rate of 5% simple interest.  Simple interest – Exercise 3 In a deposit of RO 4,000 fetched you an interest of RO 360 in a period of 3 years then calculate the rate of interest on such deposit.  Simple interest – Exercise 4 If you have to make 2 different deposits as follows: Bank Muscat: RO 5,000 deposit @ 5% simple interest per annum Bank Ahli: RO 2,500 deposit @ 4% simple interest per annum Suppose your target interest amount is RO 500, what will be the time period of deposit for both banks?  Simple interest – application on other financial products Bonds, Debentures & Loan notes issued by large corporations for borrowing money from public at large. Interest is paid monthly, quarterly, half yearly or annually The principal amount (face value amount) is returned back after the completion of time period with or without premium depending on the terms and conditions. Interest rates offered by such products is usually more than the bank rate. https://d1whtlypfis84e.cloudfront.net/guides/wp- content/uploads/2018/03/24062722/debenture.jpg Traded in financial markets so have a market price too.  Simple interest – application on other financial products For example: You have Solution: Note that interest is half yearly and to be calculated purchased 60, 10 years, on the face value of bonds. 5% Bonds of Omantel 60 indicates number of bonds, 10 years indicate the life of bonds, 5% indicates the rate of interest per annum, RO 100 is the having a face value of face value of each bond and RO 120 is the current market price RO 100 each at a market of each bond. price of RO 120 each. Calculation of interest that will be received every half yearly or Interest is paid half 6 months yearly on such bonds. P = 60 x 100 = RO 6,000 Calculate the amount of r = 5/100 = 0.05 t = 6 months = 6/12 interest that will be Interest received every 6 months = 6,000 x 0.05 x 6/12 = RO 150 received by you on such So interest received every year will be RO 300 (150 + 150) bonds every 6 months. Interest received over the term of the bonds will be RO 3,000 (300 x 10) Simple interest – application on other financial products – Ex 5 Ahmed purchased 50, 10% Regent bonds with face value RO 500 each and market price of RO 600 each. Interest on such bonds is paid quarterly i.e. every 3 months. Considering the remaining life of these bonds is 5 years. You are required to calculate the following: a. Interest received quarterly (Ans = RO 625) b. Interest received annually (Ans = RO 2,500) c. Interest received over the remaining life of such bonds (Ans = RO 12,500) Compound Interest: interest is not only calculated on outstanding principal amount but also on the interest accumulated from the previous period. interest is compounded ‘n’ number of times in a year compounding factor i.e. ‘n’ will be considered as follows: Annually: n = 1 Semi-annually: n=2 Quarterly: n = 4 Monthly: n = 12 Daily: n = 365 or 366 Compound Interest: Interest calculation: 𝒓 𝒏𝒕 Interest (I) = P (𝟏 + ) - P 𝒏 P = Principal amount of money deposited or borrowed r = rate of interest n = number of times interest compounded in a year t = time period Compound Interest: Example The amount of interest received with a deposit of RO 500 @ 12% compound interest for 2 years if compounded a. Annually b. Semi-annually c. Quarterly d. Monthly will be as follows: P = RO 500 r = 12 ÷ 100 = 0.12 t = 2 years n = depends on number of times compounded in a year it can be Annually: n = 1 Semi-annually: n=2 Quarterly: n = 4 Monthly: n = 12 𝒓 Formula for Interest (I) = P (𝟏 + )𝒏𝒕- P 𝒏 𝟎.𝟏𝟐 If compounded annually: I = 500 (𝟏 + )𝟏𝒙𝟐 - 500 = RO 127.2 𝟏 𝟎.𝟏𝟐 𝟐𝒙𝟐 If compounded semi-annually: I = 500 (𝟏 + ) - 500 = RO 131.24 𝟐 𝟎.𝟏𝟐 𝟒𝒙𝟐 If compounded quarterly: I = 500 (𝟏 + ) - 500 = RO 133.385 𝟒 𝟎.𝟏𝟐 𝟏𝟐𝒙𝟐 If compounded monthly: I = 500 (𝟏 + ) - 500 = RO 134.867 𝟏𝟐 Compound Interest: Exercise 6 A bank is offering a fixed Solution: deposit scheme for 5 years P = to be assumed to RO 1000 r = 0.12 & 0.125 under the following schemes. t = 5 years At 12%, where interest is n = depends on number of times compounded in a year it is: compounded monthly Annually: n = 1 Monthly: n = 12 At 12.5% where interest is compounded annually Option 1: 1000 〖(1+(0.12)/12)〗^12x5 - 1000 = RO 816.70 State which scheme is more Option 2: 1000 〖(1+(0.125)/1)〗^1x5 - 1000 = RO 802.032 beneficial? Suggestion: Option 2 is better than Option 1 as it earns more interest. Compound Interest: Exercise 7 In general all banks are accepting deposits @ 5% interest compounded monthly except a bank which is ready to pay interest @ 5.25% simple interest. Suggest which option is more suitable to the customer who wishes to keep money in the bank for a period of 4 years Compound Interest: Exercise 8 Find the amount to be deposited initially, if RO 420 interest is received on such loan @10% compounded yearly for a period of 2 years. (Ans: RO 2,000) Compound Interest: Exercise 9 Ali borrowed RO 1000 from a bank for 4 years with a simple interest of 5% and invested the same with an interest of 6% to be compounded quarterly for 4 years. How much will he be benefited with such arrangement? Comparison between Simple interest and Compound interest method: Principal amount or present value = RO 1000, Interest rate = 7% Period/years Simple Interest Compound Interest (t) Interest Future value Interest Future value Pxrxt P (1 + rt) 𝑟 P (1 + 𝑛)𝑛𝑡 - P 𝑟 P (1 + 𝑛)𝑛𝑡 0 1,000 1,000 - - 1 1,070 1,070 70 70 2 1,140 1,144.9 140 144.9 3 1,210 1,225.04 210 225.04 4 1,280 1,310.80 280 310.80 5 1,350 1,402.22 350 402.22 6 1,420 1,500.73 420 500.73 7 1,490 1,605.78 490 605.78 … … Rule of 72: As an investor you might easily think of the time period which will allow your investment amount to double at a given rate of interest. Though one can use the future value formula given above, there is a common tool used in finance to estimate such time period referred to as ‘Rule of 72’. Approximate time period as per ‘Rule of 72’ assuming given rate of interest compounded annually will be: 𝟕𝟐 = 𝑹𝒂𝒕𝒆 𝒐𝒇 𝒊𝒏𝒕𝒆𝒓𝒆𝒔𝒕 Rule of 72: For e.g. if the rate of interest is 8% then approximate number of 𝟕𝟐 years taken to double the investment will be = = approx.. 9 𝟖 years Also note that there is a high estimation error with this rule when the rate of interest is very low or very high interest rates. Rule of 72: Exercise 10 How long will it take for an amount deposited with a bank to double if the interest is received @ 4.5% per annum using Rule of 72? Solution: 𝟕𝟐 𝟕𝟐 = = approx.. 16 years 𝑹𝒂𝒕𝒆 𝒐𝒇 𝒊𝒏𝒕𝒆𝒓𝒆𝒔𝒕 𝟒.𝟓 Rule of 72: Exercise 11 If you want your investment to double in 6 years then what should be the rate of interest or return on such investment? Solution: 𝟕𝟐 = 6 years 𝑹𝒂𝒕𝒆 𝒐𝒇 𝒊𝒏𝒕𝒆𝒓𝒆𝒔𝒕 72 Rate of interest = = approx.. 12% 6 Rule of 72: Exercise 12 Calculate the number times your investment will grow using Rule of 72 at a rate of return of 12% in 18 years? Solution: 𝟕𝟐 Amount will double in = 6 years 𝟏𝟐 Given the investment doubles in 6 years, given period of 18 years 𝟏𝟖 will let the investment grow = 3 times 𝟔 Rule of 72: Exercise 13 Sajid got an offer letter for a job that will pay him a salary of RO 1,000 per month with an annual increment of 18% whereas his friend Tariq got an offer letter for a similar job that will pay him a salary of RO 2000 with an annual increment of 6%. 12 years from now who will receive a higher salary if they continue to stay in the same jobs? Solution: 𝟕𝟐 Sajid: As per Rule of 72 it will take = approx... 4 years for his salary to 𝟏𝟖 double and after 12 year his salary will become 1,000 x 23 = RO 8,000 𝟕𝟐 Tariq: As per Rule of 72 it will take = approx... 12 years for his salary to 𝟔 double and after 12 year his salary will become 2,000 x 2 = RO 4,000 Sajid will receive more than Tariq Additional exercises: 1. Amin gave his friend Saheem RO 5,000 stating him to pay back RO 10,000 in 7 years’ time. If interest is compounded semiannually then find the rate of compound interest charged. (Ans:10%) 2. Zubin invested some amount @ of 4 % p.a. simple interest for 3 years and received a total of RO 11,200 at the end of 3 years. He kept aside the interest amount and invested the same amount @10% compound interest for next 4 years. If interest is compounded annually, then find the amount he received at the end of 4 years for his second investment. Also calculate the total amount of interest received by him for both the investments. (Ans: Principal: RO 10,000, Total interest: RO 5,841) 𝟑 3. When all banks giving interest @ 8𝟒 % compounded every 3 months, one bank comes up 𝟏 with a scheme of simple interest @ 9𝟒 % p.a.. Calculate the option that will be beneficial to the customer for an investment of 4 years. (Ans: compound interest is a better deal than simple interest) Additional exercises: 4. A bank offers fixed deposit for 5 years under the following schemes: I. Interest @ 15% compounded half yearly II. Interest @ 14.75% compounded quarterly State which scheme is more beneficial to the customer? (Ans: II better than I) 5. Find the deposited amount if RO 420 interest is received after 2 years. Interest is calculated @ 10% compounded annually. (Ans:RO 2,000) 6. Ronald gave to Donald RO 8,000 as a friendly loan. Donald agreed to return back RO 10,000 after 12 months. If interest is compounded semiannually then calculate the rate of interest charged in the given deal. (Ans: 23.6%) 7. Mahek invested in a scheme RO 6,000 and received twice the amount in 102 months. Calculate the rate of interest if interest is compounded quarterly. (Ans:8.4%) 8. If after 36 months, Rachel got RO 2,612 for her investment at 9% compounded quarterly. Find the amount invested by Rachel. (Ans: RO 2,000) Additional exercises: 9. Find the principal amount if the interest amount received after 2 years is RO 832. Note that interest is compounded annually @ 8%. (Ans: RO 5,000) 10. Sameer deposited RO 2,000 in a bank scheme which provides 10% interest compounded 4 times in a year. How much amount will be received by him after 9 months? Also state the amount of interest earned by him in such scheme. (Ans:RO 2,153.78 & RO 153.78) 11. How long will it take for an amount deposited with a bank to double if the interest is received @ 9% per annum using Rule of 72? (Ans: 8 years) 12. Calculate the number times your investment will grow using Rule of 72 at a rate of return of 12% in 12 years? (Ans: 2 times) 13. Zeeshan got an offer letter for a job that will pay him a salary of RO 1,000 per month with an annual increment of 9% whereas his friend Tariq got an offer letter for a similar job that will pay him a salary of RO 2000 with an annual increment of 3%. 12 years from now who will receive a higher salary if they continue to stay in the same jobs? (Ans: Both will receive the same) References and other readings: Introduction to Finance by RONALD W. MELICHER & EDGAR A. NORTON; EPUB: 978-1-119-32111-8 Fundamentals of Finance - Financial institutions and markets, personal finance, financial management by Andrea Bennett, Jenny Parry and Carolyn Wirth ISBN: 978–0–9941325–2–9