When changing any conditions of an investment or loan, the amount or principal will also change.

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Florence Payne
5 years ago
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2 KEY CONCEPTS When changing any conditions of an investment or loan, the amount or principal will also change. Doubling an interest rate or term more than doubles the total interest This is due to the effects of compounding. The more frequent the compounding period, the greater the effects of any changes to the investment or loan.

3 EXAMPLE Effect of Interest Rate and Principal Investment Tyler wants to have $5000 in six years time. 4 / 00 = 0.04 (a) How much would Tyler need to invest today at 4% per year, compounded quarterly? USING A SCIENTIFIC CALCULATOR Use present value formula!!! A = 5000 i = r / N = 0.04 / 4 = 0.0 Represents quarterly compounding n P A( i) P 5000( 0.0) 24 P 5000(.0) P 5000(0.7876) P $ n = yn = 6(4) = 24 Tyler will need to invest $ to have $5000 in six years.

4 EXAMPLE Effect of Interest Rate and Principal Investment Tyler wants to have $5000 in six years time. (a) How much would Tyler need to invest today at 4% per year, compounded quarterly? USING THE TVM SOLVER # of years x # of payments Represents that only one payment is made in six years N = 6 x 6 I% = 4 PV = PMT = 0 FV = 5000 P/Y = paid out C/Y = 4 Interest is compounded quarterly Tyler will need to invest 4x per year $ to have $5000 in six years. Press ALPHA then ENTER Negative value represent money being

5 EXAMPLE Effect of Interest Rate and Principal Investment Tyler wants to have $5000 in six years time. 4.5 / 00 = (b) How much would Tyler need to invest today at 4.5% per year, compounded quarterly? USING A SCIENTIFIC CALCULATOR Use present value formula!!! A = 5000 i = r / N = / 4 = Represents quarterly compounding n P A( i) P 5000( 0.025) 24 P 5000(.025) P 5000(0.7645) P $ n = yn = 6(4) = 24 Tyler will need to invest $ to have $5000 in six years.

6 EXAMPLE Effect of Interest Rate and Principal Investment Tyler wants to have $5000 in six years time. (b) How much would Tyler need to invest today at 4.5% per year, compounded quarterly? USING THE TVM SOLVER # of years x # of payments Represents that only one payment is made in six years N = 6 x 6 I% = 4.5 PV = PMT = 0 FV = 5000 P/Y = paid out C/Y = 4 Interest is compounded quarterly Tyler will need to invest 4x per year $ to have $5000 in six years. Press ALPHA then ENTER Negative value represent money being

7 EXAMPLE Effect of Interest Rate and Principal Investment Tyler wants to have $5000 in six years time. (a) How much would Tyler need to invest today at 4% per year, compounded quarterly? Tyler will need to invest $ to have $5000 in six years. (b) How much would Tyler need to invest today at 4.5% per year, compounded quarterly? Tyler will need to invest $ to have $5000 in six years. (c) What effect did the higher interest rate have on the Principal investment? The higher interest rate caused the Principal investment to be smaller At a higher interest rate, Tyler would make a smaller deposit to obtain the same amount after six years

8 EXAMPLE 2 Investments Kendra deposited $500 into an investment fund that has historically earned 0.7% per year, compounded annually. She intends to leave the money in the fund for at least five years. Use the TVM Solver to answer the questions below.

9 EXAMPLE 2 Investments Kendra deposited $500 into an investment fund that has historically earned 0.7% per year, compounded annually. She intends to leave the money in the fund for at least five years. Use the TVM Solver to answer the questions below. 5 x = = $33.20 # of years x # of payments Represents that only one payment is made in five years Negative value represent money being paid out Press ALPHA then ENTER Interest is compounded annually x per year

10 EXAMPLE 2 Investments Kendra deposited $500 into an investment fund that has historically earned 0.7% per year, compounded annually. She intends to leave the money in the fund for at least five years. Use the TVM Solver to answer the questions below. 5 x 5 2 x = = $88.45 # of years x # of payments Represents that only one payment is made in five years Negative value represent money being paid out Press ALPHA then ENTER Interest is compounded annually x per year

11 EXAMPLE 2 Investments (continued) Did doubling the interest rate more than double the total interest? YES! = = $33.20 = = $88.45

12 EXAMPLE 3 Using Technology to Compare Compounding Periods Anna has $2000 available to invest at 2% per year, compounded annually. She will need the money in six to eight years to finance her children s education. (a) Graph the relation A = 2000(.2) n Press 2 nd Y= 4:PlotsOff Enter (this will clear any graphs) Press WINDOW and enter the settings shown on the right Press Y= (clear any equations by pressing CLEAR) For Y, enter 2000(.2)^X ( X can be entered by pressing the key) Press GRAPH. Sketch and label the graph on the axes provided. Amount ($) # of years

EXAMPLE 3 Using Technology to Compare Compounding Periods (b) Use the CALC function to determine A for the following: Press 2 nd Trace :Value (i) X = 6 (for 6 years) (ii) X = 7 (for 7 years) A =

13 EXAMPLE 3 Using Technology to Compare Compounding Periods (b) Use the CALC function to determine A for the following: Press 2 nd Trace :Value (i) X = 6 (for 6 years) (ii) X = 7 (for 7 years) A = $ A = $ (iii) X = 8 (for 8 years) A = $ (c) What happens to the graph as the number of years increases? The curve increases and gets steeper Example of exponential relation Amount ($) # of years

14 Homework: Page # 9, 2, 4, 7

Financial institutions pay interest when you deposit your money into one of their accounts.

KEY CONCEPTS Financial institutions pay interest when you deposit your money into one of their accounts. Often, financial institutions charge fees or service charges for providing you with certain services