Introduction to the Compound Interest Formula

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1 Introduction to the Compound Interest Formula Lesson Objectives: students will be introduced to the formula students will learn how to determine the value of the required variables in order to use the formula 1

2 INTEREST -- what is it? INTEREST RATE -- what is it? A rate charged or paid for the use of money. An interest rate is often expressed as an annual percentage of the PRINCIPAL. savings/premium rate savings compare.html calculator/ 2

3 DEFINITIONS PRINCIPAL (P) is the sum of money deposited or borrowed INTEREST (I) is the money charged for the use of the principal RATE PER ANNUM (r) is the interest charged per year expressed as a percentage of the principal annum = year TIME (t) is the length of time on which the interest is charged AMOUNT (A) is the sum of money to be repaid including the interest and the principal When someone needs money to purchase something such as a home or a car this money can be borrowed. The rent for the use of this money is called INTEREST. Interest is the charge over and above what is borrowed. Present Value (PV) = the current value of a loan or investment Future Value (FV) = the value of an investment/ loan at the end of the term Depreciation = the amount that the value of an item decreases over time Creditor = a person / institution that lends money Compound interest is interest calculated on the principal amount invested, which is then added to the principal amount, and compounded again. Compound interest can be earned daily, weekly, monthly or yearly. Generally the more times an amount is compounded, the more money you can make. Simple Interest appelet 3

4 COMPOUND INTEREST: Exponential growth Prerequisite Skill: SIMPLE INTEREST Simple Interest is a fee paid on a loan or investment it is a percent of the Principal it is calculated on the Initial Value (PRINCIPAL= P) at an annual interest rate, r, (expressed as a decimal) for a period of time, t ( expressed in years) To calculate the interest paid on an initial amount (P) use... I P r t where: r is the Interest rate (%) as a decimal t is time in units of YEARS 4

5 The AMOUNT repaid, A, is the original amount borrowed, PRINCIPAL, PLUS interest A = P + I A = P + Prt since I = Prt, you can substitute the I for Prt factor out the P from both terms A = P (1 + rt) 5

6 EXAMPLES: Calculate how much Interest in earned if $2000 is invested at 4% per annum for 26 weeks. GIVEN : P = $2000 r = 4% = t = 26 weeks = UNKNOWN : I =? EQUATION: SOLVE: 6

7 Find the Amount to be repaid if $575 is borrowed for 6 months at an annual interest rate of 12% GIVEN: P = $575 r = 12% or 0.12 t = 6 months or 0.5 yrs UNKNOWN: A amount repaid EQUATION: A = P + I or A = P + Prt or A = P( 1 + rt) WHICH ONE DO YOU CHOOSE?????? How much INTEREST was charged on the original amount? 7

8 Say you deposited $1000 in the bank, calculate the interest earned over a 5 year period using an annual interest rate of 7.3% interest rate. 8

COMPOUND INTEREST: introduction the equation: the variables: A = the accumulated amount or FUTURE VALUE P = the Principal, initial value or PRESENT VALUE of the loan or

9 COMPOUND INTEREST: introduction the equation: the variables: A = the accumulated amount or FUTURE VALUE P = the Principal, initial value or PRESENT VALUE of the loan or investment i = interest rate per compounding period n = total number of compounding periods it is the # of compounding periods in one yr multiplied by the total number of years. 9

10 TERMINOLOGY: PERIODS THAT INTEREST CAN BE COMPOUNDED also called COMPOUNDING PERIODS ANNUALLY: once a year 0 12 SEMI ANNYALLY: 2 a year or every 6 months QUARTERLY: 4 times a year or every 3 months MONTHLY: every month or 12 times a year WEEKLY : every week or 52 times a year BI WEEKLY: every 2 weeks or 26 times a year DAILY : every day or 365 times a year 10

11 To Calculate "i" annual interest rate as a decimal (not %) # of compounding periods in 1 year For example: Find "i" as it would appear in the Compound Interest Formula 4.5% compounded semi annually 5 1/4% compounded monthly 8% compounded annually 2.4% compounded daily 11

12 To determine "n" as it would appear in the C. I. Formula... "n" = It is the TOTAL number of times interest will be compounded over a specified period of time ie. length of a loan every month (monthly) for 2 years weekly for 18 months bi weekly for 3 years 12

13 EXAMPLE: An education fund has an initial amount of $5000. Interest is compounded quarterly at 6% per year for a total of 10 years. State the values of P, i, and n P = the initial amount i = interest at each compounding period n = total number of compounding periods 13

14 i = %rate #comp per. in 1 year n= total # times interest is compounded (added) 14

Chapter 3 Mathematics of Finance

Chapter 3 Mathematics of Finance Section R Review Important Terms, Symbols, Concepts 3.1 Simple Interest Interest is the fee paid for the use of a sum of money P, called the principal. Simple interest