BUS 250 Seminar 7 Key Terms

BUS 250 Seminar 7

Key Terms • Interest period: the amount of time which interest is calculated and added to the principal. • Compound interest: the total interest that accumulated after more than one interest period. • Future value, maturity value, compound amount: the accumulated principal and interest after one or more interest periods. • Period interest rate: the rate for calculating interest for one interest period-the annual interest rate is divided by the number of periods per year.

Find the period interest rate for: • A 12% annual interest rate with 4 interest periods per year. • 3% • An 18% annual rate with 12 interest periods per year. • 1½% • An 8% annual rate with 4 interest periods per year. • 2%

Look at this example Find the future value of a loan of $800 at 13% for three years. • The period interest rate is 13% since it is calculated annually. • First end-of-year = $800 x 1. 13 = $904 • Second end-of-year =$904 x 1. 13 = $1021. 52 • Third end-of-year = $1021. 52 x 1. 13 = $1, 154. 32 • The FV of this loan is $1, 154. 32

Find the FV of an investment • Principal = $10, 000 • 8% annual interest rate, compounded semiannually • Find the FV at the end of three years. • Find the period interest rate: 8% ÷ 2 = 4% • Determine number of periods: 3 x 2 = 6 • Calculate each end-of-period principal. • Period 1 = 10, 000 x 1. 04 = $10, 400

• Find the FV of an investment= Second end-of-period principal $10, 400 x 1. 04 = $10, 816 • Calculate each end-of-principal through the sixth end-of-period principal. • What is the final end-of-principal amount? • $12, 653. 19

13. 1. 2 Using a $1. 00 FV Table • Since it would be tedious and timeconsuming to calculate a large number of periods with the previous method, we can use Table 13 -1, which is the future value or compound amount of $1. 00. • Find the number of periods and the rate period to identify the value by which the principal is multiplied.

Try this example • Using Table 13 -1, find the future value and compound interest on $2, 000 invested for four years compounded semiannually at 8%. • FV = $2, 737. 14 • CI = $737. 14 • What would the simple interest be for the same loan? • $640

13. 1. 3 Find the Future Value and Compound Interest Using a Formula (optional) • The future value formula is: FV = where FV is the future value, P is the principal, R is the period interest rate, and N is the number of periods. • The formula for finding future value will require a calculator that has a power function.

Try this example • Find the future value and compound interest of a 3 -year $5, 000 investment that earns 6% compounded monthly. • FV = $5, 983. 40 • CI = $5, 983. 40 – $5, 000 = $983. 40

13. 1. 4 Find the Effective Interest Rate • Effective interest rate is also called the annual percentage yield or APY when identifying rate of earning on an investment. • It is called APR, annual percentage rate, when identifying the rate of interest on a loan. • Effective rate: the equivalent simple interest rate that is equivalent to a compound rate

Look at this example • Marcia borrowed $600 at 10% compounded semiannually. What is the effective interest rate? • Using the manual compound interest method: • Period rate interest = 10% / 2 = 5% = 0. 05 • First end-of-period principal = $600 x 1. 05 = $630 • Second end-of-principal = $630 x 1. 05 =$661. 50 • Compound interest after first year = $61. 50

Effective interest rate Annual effective interest rate = $61. 50 $600 Multiplied by 100% = 0. 1025 x 100% = 10. 25% Using the table method (Table 13 -1): The table value is 1. 10250. Subtract 1. 00 and multiply by 100%. The effective rate is 10. 25%

13. 2 Present Value • Find the present value based on annual compounding for one year. • Find the present value using a $1. 00 present value table. • Find the present value using a formula (optional).

Present value • The simplest case would be annual compounding interest for one year: the number of interest periods is 1 and the period interest rate is the annual interest rate. • Principal (present value) = future value 1 + annual interest rate* * denotes decimal equivalent

Look at this example • Find the amount of money that The 7 th Inning needs to set aside today to ensure that $10, 000 will be available to buy a new large screen plasma television in one year if the annual interest rate is 4% compounded annually. • PV = 10, 000 1. 04 = $9, 615. 38 • An investment of $9, 615. 38 at 4% would have a value of $10, 000 in one year.

Try these examples • Calculate the amount of money needed now to purchase a laptop computer and accessories valued at $2, 000 in a year if you invest the money at 6%. • $1, 886. 79 • John wants to replace a tool valued at $150 in a year. How much money will he have to put into a savings account that pays 3% annual interest? • $145. 63

13. 2. 2. Use a $1. 00 Present Value Table • Using a present value table is the most efficient way to calculate the money needed now for a future expense or investment. • Table 13 -3 shows the present value of $1. 00 at different interest rates for different periods.

Look at this example • The 7 th Inning needs $35, 000 in 4 years to buy new framing equipment. How much should be invested at 4% interest compounded annually? • 4 periods at 4% shows a value of 0. 85480 • Multiply this value by $35, 000 • The result is $29, 918 • They must invest $29, 918 at 4% compounded annually for four years to have $35, 000

Try these examples • How much money would you have to invest for 5 years at 6% paid semi-annually to make a down payment of $20, 000 on a house? • $14, 881. 80 • How much money would you have to invest for 3 years at 10% paid semi-annually to purchase an automobile that costs $20, 000? • $14, 924. 40

13. 2. 3 Find the Present Value Using a Formula (optional) • The present value formula is: PV = where PV is the present value, FV is the future value, R is the period interest rate, and N is the number of periods.

Try this example • Find the present value required at 5. 2% compounded monthly to total $8, 000 in three years. • PV = • Period int. rate = 5. 2%/12 =. 0043333333 • PV = = $6, 846. 78