compound interest - lecture 21 section 10people.hsc.edu/faculty-staff/robbk/math111/lectures/spring...

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


Outline

1 Compound Interest



4 The Rule of 72


6 Assignment


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.


Compound Interest

Example (Compound Interest)A principal of $1000 is invested at 6% interest compoundedannually for 3 years.Find the future value.


Outline

1 Compound Interest



4 The Rule of 72


6 Assignment


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.


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?


Outline

1 Compound Interest



4 The Rule of 72


6 Assignment


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.



Example (Effective Interest Rate)Find the effective interest rate, or APY, of 12% compounded

Annually

SemiannuallyQuarterlyMonthlyDailyHourlyMinutelySecondly

Do you notice a trend?




AnnuallySemiannually

QuarterlyMonthlyDailyHourlyMinutelySecondly





AnnuallySemiannuallyQuarterly

MonthlyDailyHourlyMinutelySecondly





AnnuallySemiannuallyQuarterlyMonthly

DailyHourlyMinutelySecondly





AnnuallySemiannuallyQuarterlyMonthlyDaily

HourlyMinutelySecondly





AnnuallySemiannuallyQuarterlyMonthlyDailyHourly

MinutelySecondly





AnnuallySemiannuallyQuarterlyMonthlyDailyHourlyMinutely

Secondly





AnnuallySemiannuallyQuarterlyMonthlyDailyHourlyMinutelySecondly



Outline

1 Compound Interest



4 The Rule of 72


6 Assignment


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?


Outline

1 Compound Interest



4 The Rule of 72


6 Assignment


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.


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%?


Outline

1 Compound Interest



4 The Rule of 72


6 Assignment


Assignment

AssignmentChapter 10: Exercises 33, 34, 37, 38, 47a-c, 49, 50.


compound interest - lecture 21 section 10people.hsc.edu/faculty-staff/robbk/math111/lectures/spring...

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