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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 exampleFind 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 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?
• $12,653.19
Find the FV of an investment
13.1.2 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 = $2,737.14• 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.
(1 )NP R
Try this example• Find the future value and compound interest
of a 3-year $5,000 investment that earns 6% compounded monthly.
• FV =
• FV =
• FV = $5,983.40
• CI = $5,983.40 – $5,000 = $983.40
(1 )NP R
365,000(1 .005)
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 rateAnnual 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 7th 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 7th 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.
(1 )NFV
R