MIME-Version: 1.0 Content-Location: file:///C:/59141A37/T102Lessons6.6spring07.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Lesson 6

Lesson 6.6<= /span>

 

Objective:  =                &= nbsp;   1.  To com= pute simple interest.

 

2.&n= bsp;        To compute compound interest.

 

 

 

An ad for a bank says that a Money Market yields 4.65% interest.  What does this mean= ?

Terms

 

Interest-is the amount of money the bank will pay for = using that money

 

Principal-the original amount deposited or borrowed.

 

Interest rate-the percent used to determine the intere= st

 

Simple interest-interest computed on the original prin= cipal

 

Example-If you borrow $800 from a bank at a simple int= erest rate of 7% for one year, then the interest is….

 

 

 

 

The amount needed to pay off the loan is….

 

 

*Interest after one year I =3D Pr

 

Interest after t years   I =3D P= rt

 

The amount in the account after t years:

 A =3D P + Prt<= /span> =3D P( 1 + rt)

 

Example:  Steve opened a savings account that pays simple interest at the rate of 5 ½= ;% per year.  If he deposits $500= 0 and makes no other deposists, find the amounts for = the following times:

 

   &nbs= p;        a.  1 yea= r        &= nbsp;           &nbs= p;            &= nbsp;            b.  3 months

 

 

 

 

 

 

 Example:=   Find the annual simple interest ra= te if a principal of $8000 yields $8340 at the end of 1 year.

 

 

 

 

 

 

 

 

Compound interest-pays interest on interest

 

Example:  If you invest $100 at 8% interest compounded quarterly, how much will you have in = the bank after l year?

 

1st quarter &nbs= p;  I =3D 100(0.08)(1/4)=3D 2

 

A =3D 100+2 =3D 102 =3D 100(1.02)

 

2nd quarter  = ;     I =3D 102(0.08)(1/4)=3D 2.04

 

A =3D 102 + 2.04 =3D 104.04 =3D 102(1.02)

 

3rd quarter  = ;     I =3D 104.02(0.08)(1/4) =3D 2.08

 

A =3D 104.04 =3D 2.08 =3D 106.12=3D 102(1.02)(1.02)

 

4th quarter  = ;      I =3D 106.12(0.08)(1/4) =3D 2.12

 

A =3D 106.12 + 2.12 =3D 108.24 =3D 102(1.02)(1.02)(1.02)

 

Formula:

Period

Initial amount

Final amount

1

100

100(1.02)

2

100(1.02)

100(1.02)(1.02) =3D100(1.02)2<= /p>

3

100(1.02)2(1.02)

100(1.02)2(1.02) =3D 100(1.02)3=

4

100(1.02)3

100(1.02)3(1.02) =3D 100(1.02)4=

 

FORMULA for computing the amount at the end of = the nth period is   A =3D P ( 1 + r)n  Note in this formula r is the interest rate per period= and n is the number of periods.

Suppose you deposit $1500 in a savings account that pa= ys 6% interest compounded monthly, what is the balance after 1 year?  What is the effective annual yield= ?

 

 

Steve loans $7500 to the owner of a new restaurant.  He will be repaid at the end of six years at 8% interest compounded quarterly.=   Find how much he will be repaid.

 

            r   &nb= sp;            =             &nb= sp;            =             &nb= sp;     n

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Interest Worksheet