Learning Goal: What is compound interest? How do we compute the interest on an investment?

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1 Name IB Math Studies Year 1 Date 7-6 Intro to Compound Interest Learning Goal: What is compound interest? How do we compute the interest on an investment? Warm-Up: Let s say that you deposit $100 into your savings account today. This bank account gains 2% interest every year. If you don t withdraw any money a. How much money would you have at the end of the first year? b. How much money would you have at the end of the second year? c. In these two years, how much interest (money) did you gain? d. Is the money in the savings account increasing by the same about each year? Interest is the percent of money charged to money borrowed or percent of money earned on an investment. When you put money into a savings account, the bank often pays you interest. That interest is the incentive for you to keep the money in the bank, your account is gaining this interest. When you are saving money When you take out a loan (or borrow money) to pay for something like a house or car you have to pay interest on that money. When you are borrowing money Compound Interest When you borrow money or deposit money interest accumulates per year (also called per annum). This means that the interest gained each year is based off the current amount of money in the account, not the original amount deposited.

2 Compound Interest with the Calculator All graphing calculators have an in-built finance program that can be used to investigate financial scenarios. This is called a TVM Solver, where TVM stands for the time value of money. The TVM Solver can be used to find any variable if all the other variables are given. TVM solver is found under the APPS button on the calculator. Press APPS For the TI-83/84, the abbreviations used are: N = total number of times the account is compounded (the number of compounding periods per year the number of years) I% = annual interest rate (kept as a percent) PV = principal (present value) PMT = monthly payment (always 0 for this class) FV = future value P/Y and C/Y = number of compounding periods per year In this course, you will be responsible for the following compound interest periods. Compound interest is the number of times you will earn interest on your investement per year (per annum). Annually Semi (Half)-Annually Quarterly Monthly A Couple of Notes In this class, you will only be solving for variables I%, PV, FV, and N. In order to show your work, you must make a key for all your substitutions in the calculator. I% is always entered as a percent, not a decimal. PV is always entered as a negative number. P/Y and C/Y will always be 1, 2, 4, or 12. To get an answer, enter the variables that you know on the appropriate lines and then scroll to the line for the variable you wish to solve for and press Alpha Enter MODEL PROBLEM: Holly invests GBP in an account that pays 4.25% per annum compounded monthly. How many GBP will be in her account after 5 years?

3 Solving for Future Value FV Remember to enter the present value as a negative number! WE TRY: John deposits $4000 into a bank YOU TRY: Morimi invested 700 JPY at 6.3% account. The bank s stated rate of interest is 6% interest compounded quarterly for 15 years. per annum compounded quarterly. Calculate the How much money did Morimi have at the end of value of John s account after 8 years. the 15th year? Solving for Present Value PV The calculator will give you the present value as a negative number. Write it as a positive #! WE TRY: Mr. Gino invested x dollars in an YOU TRY: Carmen deposited Argentine pesos, account that pays a nominal annual interest rate of ARS, in a bank account which pays a nominal 3.6% compounded sem-annually in order to buy a interest rate of 17%, compounded yearly. After speedboat. After 18 years, he will have $35,300 three years, the total amount in Carmen s account in the account. Calculate the value of x. is 10,000 ARS. Find the amount that Carmen deposited in the bank account.

4 Solving for Interest Rate Remember to enter the present value as a negative number! WE TRY: Jacob invested EUR for YOU TRY: At what interest rate, compounded 30 years. The investment has a nominal annually, would you need to invest $100 in order annual interest rate r% and is compounded to have $125 in 2 years? annually. After 30 years, the investment will be worth EUR. Calculate the value of r to the nearest percent. 1. Samantha puts in a bank account earning 6% annual interest compounded monthly. How much total money will she have after 20 years? Practice 2. Michael wants to make an investment and accumulate 25,000 EUR over a period of 18 years. He finds an investment option that earns a nominal interest rate of 8% compounded quarterly. Find the amount of money that Michael will have to invest to have 25,000 EUR at the end of 15 years. 3. You are planning to send your daughter to college in 18 years. You determine that in the end you will need $100,000 in order to pay for tuition, room and board, etc. At what interest rate, compounded annually, would you need to invest $20,000 in order to reach your goal in 18 years?

5 Name Lesson 7-6 Homework Date 1. Carla has 7000 dollars to invest in a fixed deposit which is compounded annually. She aims to have dollars after 10 years. Calculate the annual interest rate needed for Carla to achieve her aim. 2. Diogo deposited 8000 Argentine pesos, ARS, in a bank account which pays a nominal annual interest rate of 15%, compounded monthly. Find how much Diogo has in his account after 2 years. 3. Jacob invested x EUR for 43 years. The investment has a nominal annual interest rate of 3.2% and is compounded quarterly. After 43 years, the investment will be worth EUR. Calculate the value of Jacob s initial investment, x. Give your answer to two decimal places.

6 4. Daniela is going for a holiday to South America. She flies from the US to Argentina stopping in Peru on the way. In Peru she exchanges 85 United States dollars (USD) for Peruvian nuevo sol (PEN). The exchange rate is 1 USD = 3.25 PEN and a flat fee of 5 USD commission is charged. (a) Calculate the amount of PEN she receives. At the end of Daniela s holiday she has 370 Argentinean peso (ARS). She converts this back to USD at a bank that charges a 4% commission on the exchange. The exchange rate is 1 USD = 9.60 ARS. (b) Calculate the number of ARS that Daniela must pay in commission. (c) Calculate the amount of USD she receives.