compound interest - lecture 21 section 10people.hsc.edu/faculty-staff/robbk/math111/lectures/spring...
Post on 21-Apr-2020
6 Views
Preview:
TRANSCRIPT
Compound InterestLecture 21
Section 10.3
Robb T. Koether
Hampden-Sydney College
Mon, Mar 16, 2015
Robb T. Koether (Hampden-Sydney College) Compound Interest Mon, Mar 16, 2015 1 / 18
1 Compound Interest
2 The Compound Interest Formula
3 The Effective Interest Rate
4 The Rule of 72
5 Certificates of Deposit
6 Assignment
Robb T. Koether (Hampden-Sydney College) Compound Interest Mon, Mar 16, 2015 2 / 18
Outline
1 Compound Interest
2 The Compound Interest Formula
3 The Effective Interest Rate
4 The Rule of 72
5 Certificates of Deposit
6 Assignment
Robb T. Koether (Hampden-Sydney College) Compound Interest Mon, Mar 16, 2015 3 / 18
Compound Interest
Definition (Compound Interest)When a loan is based on compound interest, interest is paid on theprincipal and on all interest accrued so far.
Definition (Compounding Period)The compounding period is the length of time over which the interest iscomputed when it is compounded.
Robb T. Koether (Hampden-Sydney College) Compound Interest Mon, Mar 16, 2015 4 / 18
Compound Interest
Example (Compound Interest)A principal of $1000 is invested at 6% interest compoundedannually for 3 years.Find the future value.
Robb T. Koether (Hampden-Sydney College) Compound Interest Mon, Mar 16, 2015 5 / 18
Outline
1 Compound Interest
2 The Compound Interest Formula
3 The Effective Interest Rate
4 The Rule of 72
5 Certificates of Deposit
6 Assignment
Robb T. Koether (Hampden-Sydney College) Compound Interest Mon, Mar 16, 2015 6 / 18
The Compound Interest Formula
If the interest is compounded annually, then
F = P(1 + r)t .
If the interest is compounded k times a year, then
F = P(
1 +rk
)kt.
Robb T. Koether (Hampden-Sydney College) Compound Interest Mon, Mar 16, 2015 7 / 18
Compound Interest
Example (Compound Interest)A principal of $1000 is invested at 8% interest compoundedquarterly for 3 years.Find the future value.How does this compare to simple interest? That is, how muchinterest is earned in one year?How does this compare to compounding annually?
Robb T. Koether (Hampden-Sydney College) Compound Interest Mon, Mar 16, 2015 8 / 18
Outline
1 Compound Interest
2 The Compound Interest Formula
3 The Effective Interest Rate
4 The Rule of 72
5 Certificates of Deposit
6 Assignment
Robb T. Koether (Hampden-Sydney College) Compound Interest Mon, Mar 16, 2015 9 / 18
The Effective Interest Rate
Definition (Effective Interest Rate)For a given compound interest rate, the effective interest rate reff, orannual percentage yield (APY), is the simple interest rate thatproduces the same yield at the end of one year.
Given an interest rate r compounded k time a year, the effectiverate is given by
APY =(
1 +rk
)k− 1.
Robb T. Koether (Hampden-Sydney College) Compound Interest Mon, Mar 16, 2015 10 / 18
The Effective Interest Rate
Example (Effective Interest Rate)Find the effective interest rate, or APY, of 12% compounded
Annually
SemiannuallyQuarterlyMonthlyDailyHourlyMinutelySecondly
Do you notice a trend?
Robb T. Koether (Hampden-Sydney College) Compound Interest Mon, Mar 16, 2015 11 / 18
The Effective Interest Rate
Example (Effective Interest Rate)Find the effective interest rate, or APY, of 12% compounded
AnnuallySemiannually
QuarterlyMonthlyDailyHourlyMinutelySecondly
Do you notice a trend?
Robb T. Koether (Hampden-Sydney College) Compound Interest Mon, Mar 16, 2015 11 / 18
The Effective Interest Rate
Example (Effective Interest Rate)Find the effective interest rate, or APY, of 12% compounded
AnnuallySemiannuallyQuarterly
MonthlyDailyHourlyMinutelySecondly
Do you notice a trend?
Robb T. Koether (Hampden-Sydney College) Compound Interest Mon, Mar 16, 2015 11 / 18
The Effective Interest Rate
Example (Effective Interest Rate)Find the effective interest rate, or APY, of 12% compounded
AnnuallySemiannuallyQuarterlyMonthly
DailyHourlyMinutelySecondly
Do you notice a trend?
Robb T. Koether (Hampden-Sydney College) Compound Interest Mon, Mar 16, 2015 11 / 18
The Effective Interest Rate
Example (Effective Interest Rate)Find the effective interest rate, or APY, of 12% compounded
AnnuallySemiannuallyQuarterlyMonthlyDaily
HourlyMinutelySecondly
Do you notice a trend?
Robb T. Koether (Hampden-Sydney College) Compound Interest Mon, Mar 16, 2015 11 / 18
The Effective Interest Rate
Example (Effective Interest Rate)Find the effective interest rate, or APY, of 12% compounded
AnnuallySemiannuallyQuarterlyMonthlyDailyHourly
MinutelySecondly
Do you notice a trend?
Robb T. Koether (Hampden-Sydney College) Compound Interest Mon, Mar 16, 2015 11 / 18
The Effective Interest Rate
Example (Effective Interest Rate)Find the effective interest rate, or APY, of 12% compounded
AnnuallySemiannuallyQuarterlyMonthlyDailyHourlyMinutely
Secondly
Do you notice a trend?
Robb T. Koether (Hampden-Sydney College) Compound Interest Mon, Mar 16, 2015 11 / 18
The Effective Interest Rate
Example (Effective Interest Rate)Find the effective interest rate, or APY, of 12% compounded
AnnuallySemiannuallyQuarterlyMonthlyDailyHourlyMinutelySecondly
Do you notice a trend?
Robb T. Koether (Hampden-Sydney College) Compound Interest Mon, Mar 16, 2015 11 / 18
The Effective Interest Rate
Example (Effective Interest Rate)Find the effective interest rate, or APY, of 12% compounded
AnnuallySemiannuallyQuarterlyMonthlyDailyHourlyMinutelySecondly
Do you notice a trend?
Robb T. Koether (Hampden-Sydney College) Compound Interest Mon, Mar 16, 2015 11 / 18
Outline
1 Compound Interest
2 The Compound Interest Formula
3 The Effective Interest Rate
4 The Rule of 72
5 Certificates of Deposit
6 Assignment
Robb T. Koether (Hampden-Sydney College) Compound Interest Mon, Mar 16, 2015 12 / 18
The Rule of 72
Definition (The Rule of 72)The Rule of 72 says that an effective rate, or APY, of r% will double thevalue of an investment in 72/r years.
An effective rate of 8% will double the value of the investment in 9years.How long will it take for the future value to grow to 8 times theprincipal? 64 times?
Robb T. Koether (Hampden-Sydney College) Compound Interest Mon, Mar 16, 2015 13 / 18
Outline
1 Compound Interest
2 The Compound Interest Formula
3 The Effective Interest Rate
4 The Rule of 72
5 Certificates of Deposit
6 Assignment
Robb T. Koether (Hampden-Sydney College) Compound Interest Mon, Mar 16, 2015 14 / 18
Certificates of Deposit
Definition (Certificate of Deposit)A certificate of deposit (CD) is an investment, usually through a bank,for a fixed period of time at a fixed compound interest rate.
There is typically a penalty for early withdrawal. The penalty isusually equal to 6 months of interest.
Robb T. Koether (Hampden-Sydney College) Compound Interest Mon, Mar 16, 2015 15 / 18
Certificates of Deposit
ExampleCertificate of Deposit
What is the future value of a 5-year CD earning 1% interest,compounded quarterly?Suppose that at the end of one year, the rate on new CDs is 2%.Should the investor cash in the CD earning 1%, pay the penalty,and reinvest the difference in a new CD earning 2%?
Robb T. Koether (Hampden-Sydney College) Compound Interest Mon, Mar 16, 2015 16 / 18
Outline
1 Compound Interest
2 The Compound Interest Formula
3 The Effective Interest Rate
4 The Rule of 72
5 Certificates of Deposit
6 Assignment
Robb T. Koether (Hampden-Sydney College) Compound Interest Mon, Mar 16, 2015 17 / 18
Assignment
AssignmentChapter 10: Exercises 33, 34, 37, 38, 47a-c, 49, 50.
Robb T. Koether (Hampden-Sydney College) Compound Interest Mon, Mar 16, 2015 18 / 18
top related