Using a Spreadsheet to Calculate the Amount Owing when using ...
Lesson 16, page 10
Foundations for College Mathematics MBF3C·B
•••••••••••••••••••••••••••••••••••••••••••••••• Support Questions (do not send in for evaluat ion)
1.
What does "interest" mean? Explain the diflerence between simple and compound interest.
2.
Calculate the amount of simple interest you would earn if you invested $4000 at a rate of 9ck per year interest, for five years.
3.
How much time would it take to earn $50 interest on an investment of $5000 if the Himple interest rate were 2%?
4.
al
Calculate the amount of money you would have at the end of each year for four years if you invested $2000 at 6(k simple inte rest.
b)
Use a chart like the one on page 7 to calculate the amount of money you would have at the end of each year for four years if you invested $2000 at 6~ compound interest.
cl
Enter the an~wers into your graphing calculator a nd create graphs to compare thP amounts of money in al and bl.
There are Suggested Answers to Support Questions at the end of this unit.
Using a Spreadsheet to Calculate the Amount Owing when using Compound Interest In this section, we're going to do a number of calculations of compound interest. That means that we're going to need a lot of those charts we made in the last section. That sounds like a lot of work, doesn 't it? Fortunately, we have computers to do the really boring work! First you have to set up the computer so that it does the work properly.
Copynght If) 2008 The Ontario Educational Commun,cntions Authonty. All nghts reserved
www.ilc.org
Foundations for College Mathematics MBF3C-B
Lesson 16, page 29
•••••••••••••••••••••••••••••••••••••••••••••••• IIJJ 5.
Support Question (do not send in for evaluation)
a)
Change your spreadsheet oxarnple to show an investment over a 20-year period of $500.00 invested at 6~ simple interest, versus $500.00 invested at 6% compounded annually. Make a sketch of th e graphs produced.
b)
Redo part a), but with a n interest rate of 80ff·. Again, sketch the graphs.
c)
What happens to the amount of money at the end of 20 years when the interest rate is increased from 6
7.
You wi~h to purchase a $14 000 motorcycle five years fr om now. How much must you invest today at an annual interest rate of 7(/c, in order to hnvc enough money to buy the motorcycle?
There are Suggested Answ ers to Support Questions at the end of this unit.
Calculating Total Interest Earned Example 1 shows that the amount of an investment of $4000 for s ix years, if interest is 7.2Ck. per year, compounded annually, would be $6070.56. How much total interest was earned? Since the original value of the investment was $4000 and the final value was $6070.56, the difference is the interest earned. $6070.56- $4000 = $2070.56 Therefore $2070.56 of interest was earned. To calculate the total interest earned, simply s ubtract the initial value from the final value. In equation form, I= A- P.
Exam ple 3 $5000 is invested for six years at an interest rate of 4.6%. a)
How much is the invPstment worth after the six years?
bl
llow much total interest was earned?
Copyright © 2008 The Ontano Educational Commun1c3t10ns Authoroty. All nghts reserved.
Foundations for College Mathematics MBF3C-B
Lesson 17, page 5
•••••••••••••••••••••••••••••••••••••••••••••••• Solution a)
A= P(l + i)"
A=? p = $5000
= 5000( 1 + 0.046)
i = 4.6lk = 0.046
~
n
6
6548.78
=6 The amount is $6548.78.
b)
I= A- P
I= $6548.78- $5000
=$1548.78 Therefore, $1548.78 of interest was earned.
Support Question (do not send in for evaluation)
8.
~mmlll~==.==-~=-~~ ~---------
Susan invests $3500 for 10 years at an interest rate of 5.6~. a}
How much money will she have after the 10 years are up?
b)
How much interest will she have earned?
Using the TVM Solver to Calculate Principal, Amount, Interest Rate, and Time As you can see, the compound interest formula is easy to use when you're calculating the amount of an investment or its present value. Unfortunately. it's quite a bit harder to use it to calculate interest rate anrl t.irnP.
www.ilc.org
Copyright © 2008 The Ontano Educational Communications Authonty. All rights reserved
Foundations for College Mathematics MBF3C-B
Lesson 17, page 9
•••••••••••••••••••••••••••••••••••••••••••••••• - - lll 9.
Support Question (do not send in for evaluation)
Use the TVM Solver to answer the following questions. a)
Calculate the amount of an investment of $5500 for six years at an interest rate of 6_5%, compounded annually.
b)
How much should you invest now in order to have $8000 in five years at an interest rate of 6%, compounded annually?
c)
How long does it take a $2000 investment to triple in value if interest is 7---
15. What is the main difference between using a debit card and using a credit card? 16. fvlatch the meanings in column one with the following terms: minimum payment, payment due date, balance owing, payment, credit available, statement balance, cash advance, credit limit.
-Meanings
--
Terms
-
al thl• amount of monl'Y that you OWl' tJw t.:r!
i
--
~~ [
Support Question {do not send in for evaluat ion)
PE---:3:>-----
17. Sarah owes $13fi6.5fi on her credit card, which charges 0.05068';? per day, compounded daily, and has a minimum payment due of :3(k of the outstanding balance. Unfortunately, Sarah cannot afford to pay any more than the minimum payment. Assuming she doesn't make additional purchases with th
Foundations for College Mathematics MBF3C·B
•••••••••••••••••••••••••••••••••••••••••••••••• Support Questions (do not send in for evaluat ion)
1.
What does "interest" mean? Explain the diflerence between simple and compound interest.
2.
Calculate the amount of simple interest you would earn if you invested $4000 at a rate of 9ck per year interest, for five years.
3.
How much time would it take to earn $50 interest on an investment of $5000 if the Himple interest rate were 2%?
4.
al
Calculate the amount of money you would have at the end of each year for four years if you invested $2000 at 6(k simple inte rest.
b)
Use a chart like the one on page 7 to calculate the amount of money you would have at the end of each year for four years if you invested $2000 at 6~ compound interest.
cl
Enter the an~wers into your graphing calculator a nd create graphs to compare thP amounts of money in al and bl.
There are Suggested Answers to Support Questions at the end of this unit.
Using a Spreadsheet to Calculate the Amount Owing when using Compound Interest In this section, we're going to do a number of calculations of compound interest. That means that we're going to need a lot of those charts we made in the last section. That sounds like a lot of work, doesn 't it? Fortunately, we have computers to do the really boring work! First you have to set up the computer so that it does the work properly.
Copynght If) 2008 The Ontario Educational Commun,cntions Authonty. All nghts reserved
www.ilc.org
Foundations for College Mathematics MBF3C-B
Lesson 16, page 29
•••••••••••••••••••••••••••••••••••••••••••••••• IIJJ 5.
Support Question (do not send in for evaluation)
a)
Change your spreadsheet oxarnple to show an investment over a 20-year period of $500.00 invested at 6~ simple interest, versus $500.00 invested at 6% compounded annually. Make a sketch of th e graphs produced.
b)
Redo part a), but with a n interest rate of 80ff·. Again, sketch the graphs.
c)
What happens to the amount of money at the end of 20 years when the interest rate is increased from 6
7.
You wi~h to purchase a $14 000 motorcycle five years fr om now. How much must you invest today at an annual interest rate of 7(/c, in order to hnvc enough money to buy the motorcycle?
There are Suggested Answ ers to Support Questions at the end of this unit.
Calculating Total Interest Earned Example 1 shows that the amount of an investment of $4000 for s ix years, if interest is 7.2Ck. per year, compounded annually, would be $6070.56. How much total interest was earned? Since the original value of the investment was $4000 and the final value was $6070.56, the difference is the interest earned. $6070.56- $4000 = $2070.56 Therefore $2070.56 of interest was earned. To calculate the total interest earned, simply s ubtract the initial value from the final value. In equation form, I= A- P.
Exam ple 3 $5000 is invested for six years at an interest rate of 4.6%. a)
How much is the invPstment worth after the six years?
bl
llow much total interest was earned?
Copyright © 2008 The Ontano Educational Commun1c3t10ns Authoroty. All nghts reserved.
Foundations for College Mathematics MBF3C-B
Lesson 17, page 5
•••••••••••••••••••••••••••••••••••••••••••••••• Solution a)
A= P(l + i)"
A=? p = $5000
= 5000( 1 + 0.046)
i = 4.6lk = 0.046
~
n
6
6548.78
=6 The amount is $6548.78.
b)
I= A- P
I= $6548.78- $5000
=$1548.78 Therefore, $1548.78 of interest was earned.
Support Question (do not send in for evaluation)
8.
~mmlll~==.==-~=-~~ ~---------
Susan invests $3500 for 10 years at an interest rate of 5.6~. a}
How much money will she have after the 10 years are up?
b)
How much interest will she have earned?
Using the TVM Solver to Calculate Principal, Amount, Interest Rate, and Time As you can see, the compound interest formula is easy to use when you're calculating the amount of an investment or its present value. Unfortunately. it's quite a bit harder to use it to calculate interest rate anrl t.irnP.
www.ilc.org
Copyright © 2008 The Ontano Educational Communications Authonty. All rights reserved
Foundations for College Mathematics MBF3C-B
Lesson 17, page 9
•••••••••••••••••••••••••••••••••••••••••••••••• - - lll 9.
Support Question (do not send in for evaluation)
Use the TVM Solver to answer the following questions. a)
Calculate the amount of an investment of $5500 for six years at an interest rate of 6_5%, compounded annually.
b)
How much should you invest now in order to have $8000 in five years at an interest rate of 6%, compounded annually?
c)
How long does it take a $2000 investment to triple in value if interest is 7---
15. What is the main difference between using a debit card and using a credit card? 16. fvlatch the meanings in column one with the following terms: minimum payment, payment due date, balance owing, payment, credit available, statement balance, cash advance, credit limit.
-Meanings
--
Terms
-
al thl• amount of monl'Y that you OWl' tJw t.:r!
i
--
~~ [
Support Question {do not send in for evaluat ion)
PE---:3:>-----
17. Sarah owes $13fi6.5fi on her credit card, which charges 0.05068';? per day, compounded daily, and has a minimum payment due of :3(k of the outstanding balance. Unfortunately, Sarah cannot afford to pay any more than the minimum payment. Assuming she doesn't make additional purchases with th
