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. 1 ½ % 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 = $ Third end-of-year = $ x 1.13 = $1, The FV of this loan is $1,154.32

Find the FV of an investment Principal = $10,000 8% annual interest rate, compounded semi- annually 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

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, Find the FV of an investment

Using a $1.00 FV Table Since it would be tedious and time- consuming 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 per 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, CI = $ What would the simple interest be for the same loan? $640

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 = FV = $5, CI = $5, – $5,000 = $983.40

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 = $630 x 1.05 =$ Compound interest after first year = $61.50

Effective interest rate Annual effective interest rate = $61.50 $600 Multiplied by 100% = x 100% = 10.25% Using the table method (Table 13-1): The table value is 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, = $9, An investment of $9, 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, 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

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 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, 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

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 = PV = = $6,846.78