Copyright ©2015 Pearson Education, Inc. All rights reserved.
Section 4.1
Simple Interest and Discount
Slide 1 - 4Copyright ©2015 Pearson Education, Inc. All rights reserved.
A fee that is charged by a
lender to a borrower for the
right to use the borrowed
funds. The funds can be used
to purchase a house, a car, or
goods that were charged on a
credit card, for example. The
interest charge typically is
expressed as an annual
percentage rate.
Slide 1 - 5
To furnish her new apartment, Maggie Chan borrowed $4000
at 3% interest from her parents for 9 months. How much
interest will she pay?
Solution:
Copyright ©2015 Pearson Education, Inc. All rights reserved.
Example1:
Thus, Maggie pays a total of $90 in interest.40003
0.03 90.4
I Prt
I
Use the formula with ,I Prt 4000, 0.03 a d , nP r
9 /12 3 / 4 years :t
Example2: Example3:
Slide 1 - 6Copyright ©2015 Pearson Education, Inc. All rights reserved.
Example 1: A= 4000 + 90 = 4090
Example 2: A= 4500 +2565= 7065
Example 3: A= 500 + 90= 590
A2.33
A
Slide 1 - 8
Interest (I), Future Value (FV: A), Present
Value (P)
Copyright ©2015 Pearson Education, Inc. All rights reserved.
Copyright ©2015 Pearson Education, Inc. All rights reserved.
Section 4.2
Compound Interest
• Compound interest is interest calculated on the initial principal and also on
the accumulated interest of previous periods of a deposit or loan.
• Compound interest can be thought of as “interest on interest,” and will make a
deposit or loan grow at a faster rate than simple interest, which is interest
calculated only on the principal amount.
Slide 1 - 10Copyright ©2015 Pearson Education, Inc. All rights reserved.
Suppose that $5000 is invested at an annual interest rate of
3.1% compounded continuously for 4 years. Find the
compound amount.
Solution:
Example:
.031(4)5000 $5660.08.rtP eA e
In the formula for continuous compounding let
and Then a calculator with an key shows that
5000, .031,P r
4.t xe
Slide 1 - 11Copyright ©2015 Pearson Education, Inc. All rights reserved.
A=9000 𝑒0.04∗5
1.22
A=9000*1.22= 10992.64
Slide 1 - 12Copyright ©2015 Pearson Education, Inc. All rights reserved.
I= PRT= 10000*.05*3= $1500
A=P+I= 10000+1500=11500
Difference between simple and compound interest
15765.25-11500= $4265.25
Slide 1 - 14Copyright ©2015 Pearson Education, Inc. All rights reserved.
Semi annually 22
2
5.060.0506
Slide 1 - 15Copyright ©2015 Pearson Education, Inc. All rights reserved.
How much do you need to invest now, to get $10,000 in 10 yearsat 8% interest rate?
PV = $10,000 / (1+0.08)10 = $10,000 / 2.1589 = $4,631.93
So, $4,631.93 invested at 8% for 10 Years grows to $10,000
Your goal is to have $2,000 in 5 Years. You can get 10%, so how much should you
start with?
PV = $2,000 / (1+0.10)5 = $2,000 / 1.61051 = $1,241.84
$1,241.84 will grow to $2,000 if you invest it at 10% for 5 years.
Copyright ©2015 Pearson Education, Inc. All rights reserved.
Section 4.3
Annuities, Future Value,
and Sinking Funds
Slide 1 - 19
A business sets up a sinking fund so that it will be able to pay
off bonds it has issued when they mature. If it deposits
$12,000 at the end of each quarter in an account that earns
5.2% interest, compounded quarterly, how much will be in the
sinking fund after 10 years?
Solution:
Copyright ©2015 Pearson Education, Inc. All rights reserved.
Example:
40
(1 ) 1
(1 .052 / 4) 112,000
.052 / 4
$624,369.81.
niS R
i
The sinking fund is an annuity, with
The future value is
12,000, .052 / 4, and R i
4(10) 40.n
So there will be about $624,370 in the sinking fund.
Copyright ©2015 Pearson Education, Inc. All rights reserved.
Section 4.4
Annuities, Present Value,
and Amortization
Slide 1 - 24
Jim Riles was in an auto accident. He sued the person at fault
and was awarded a structured settlement in which an
insurance company will pay him $600 at the end of each
month for the next seven years. How much money should the
insurance company invest now at 4.7%, compounded monthly,
to guarantee that all the payments can be made?
Solution:
Copyright ©2015 Pearson Education, Inc. All rights reserved.
Example:
841 (1 ) 1 (1 .047 /12)600 $42,877.44.
.047 /12
niP R
i
The payments form an ordinary annuity. The amount needed to
fund all the payments is the present value of the annuity. Apply the
present-value formula with
(the interest rate per month).
600, 7 12 84, and .047 /12R n i
The insurance company should invest