Chapter Nineteen Compound Interest and Present Value - PowerPoint Presentation

Slide1

Chapter Nineteen

Compound Interest and Present Value

Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.

McGraw-Hill/IrwinSlide2

Compare simple interest with compound interest.

Calculate the compound amount and interest manually, using algebraic formulas and with a financial calculator.Explain and compute the effective rate (APY).LU 19-1: Compound Interest (Future Value) – The Big PictureLearning unit objectivesLU 19-2: Present Value -- The Big Picture

Compare present value (PV) with compound interest (FV).

Compute present value using algebraic formulas and with a financial calculator.

Check the present value answer by compounding.

19-2Slide3

Compound Interest (Future Value)

Compound Interest – The interest on the principal plus the interest of prior periodsCompounding – Involves the calculation of interest periodically over the life of the loan or investment

Present Value – The value of a loan or investment today

Future Value (compound amount) –

The final amount of the loan or investment at the end of the last period

19-3Slide4

Compounding Terms

Compounding Periods Interest CalculatedCompounding Annually Compounding Semiannually Compounding Quarterly Compounding Monthly Compounding Daily

Once a year

Every 6 months

Every 3 months

Every month

Every day

19-4Slide5

Future Value of $1 at 8% for Four Periods (Figure 19.1)

Number of periodsCompounding goes from present value to future value

Present

value

After 1 period, $1 is worth $1.08

After 2 periods, $1 is worth $1.17

After 3 periods, $1 is worth $1.26

Future Value

After 4 periods, $1 is worth $1.36

$1.00

$1.08

$1.1664

$1.2597

$1.3605

19-5Slide6

Tools for Calculating Compound Interest

Number of periods (N) Number of years multiplied by the number of times the interest is compounded per yearRate for each period (I) Annual interest rate divided by the number of times the interest is compounded per year

If you compounded $1 for 4 years at 8% annually,

semiannually, or quarterly, what is

N

and

I

?

Annually:

Semiannually:

Quarterly:

Periods

Rate

19-

6

4 x 1 = 4

4 x 4 = 16

4 x 2 = 8

8% ÷ 1 = 8%

Annually:

Semiannually:

Quarterly:

8% ÷ 4 = 2%

8% ÷ 2 = 4%Slide7

Simple Versus Compound Interest

Bill Smith deposited $80 in a savings account for 4 years at an annual interest rate of 8%. What is Bill’s simple interest and maturity value?I = P x R x TI = $80 x .08 x 4I = $25.60MV = $80 + $25.60MV = $105.60

Bill Smith deposited $80 in a savings account for 4 years at an annual interest rate of 8%. What is Bill’s interest and compounded amount?

Interest: $108.83 -- $80.00 =

$28.83

19-

7

Simple

CompoundedSlide8

Calculating Compound Amount using formula

Step 1. Find the periods n: Years multiplied by number of times interest is compounded in 1 year.Step 2. Find the rate i: Annual rate divided by number of times interest is compounded in 1 year.

Step 3. Plug the PV amount, n, and i into the following formula: FV = PV(1 + i)

n

Step 4

. Solve. This gives the compound amount.

19-

8Slide9

Calculating Compound Amount using the compound interest formula

19-9Bill wants to know the value of $80 in 4 years at 8%. He begins by identifying the PV, n, and i:PV = $80n = 4 (4 years x 1 compounding period per year)i = 8% (8% divided by 1 compounding period)

Calculator keystrokes for this problem are:(1

+

.08)

y

x

4

x

80

=

$108.84Slide10

Calculating compound amount using YOUR TI BA II PLUS calculator

Remember to clear the TVM each time you work with new data: 2ND CLR TVMTo solve the future value of $80 at 8% compounded annually for 4 years, using your calculator, follow these steps:Step 1: Input 4 and then press N.Step 2: Input 8 and then press I/Y.Step 3: Input 80, press +/- and then press

PV.Step 4: Input 0, and then press PMT.

Step 5: Press

CPT

FV

=

108.84

19-

10Slide11

Compounding (fv)figure 19.2

19-11Slide12

CALCULATING THE COMPOUND INTEREST

FV – PV = Compound interest19-12$108.84 - $80.00 = $28.84Slide13

Nominal versus Effective Rates annual Percentage yield (APY)

Truth in Savings LawAnnualPercentageYield

Effective rate (APY)

4

=

Interest for 1 year

Principal

Nominal Rate (stated rate) –

The rate on which the bank calculates interest

19-

13Slide14

Calculating Effective Rate (APY)

19-14Slide15

Nominal and Effective Rates (APY) of Interest Compared (Figure 19.3)

19-15Slide16

Present Value of $1 at

8% for Four Periods (Figure 19.4)19-16Slide17

Relationship of compounding (fv) to Present value (pv) – bill smith example

19-17Slide18

Calculating Present Value

using formulaStep 1. Find the periods n: Years multiplied by number of times interest is compounded in 1 year.Step 2. Find the rate i: Annual rate divided by number of times interest is compounded in 1 year.

Step 3. Plug the FV amount,

n

, and

i

into the following formula:

Step 4

. Solve. This gives the present value.

19-

18

PV = FV

(1 + i)

nSlide19

Calculating Present Value using formula

Since Bill knows the bike will cost $108.84 in the future, he completes the following calculation:PV = $108.84/(1 + .08)4 = $80.00Calculator keystrokes for this problem are:(1

+ .08) yx 4

= STO

1 108.84

÷ RCL

1

=

$80.00

19-

19Slide20

Calculating Present Value using A FINANCIAL CALCULATOR

19-20Step 1: Input 4 and then press N.Step 2: Input 8 and then press I/Y.Step 3: Input 108.84 and then press FV.Step 4: Input 0 and then press

PMT.Step 5: Press CPT

PV

=

-80.00

Remember to clear the TVM each time you work with new data: 2ND CLR TVM

Since Bill knows the bike will cost $108.84 in the future, he completes the following calculation:Slide21

Comparing Compound Interest (FV) with Present Value (PV)

19-21Slide22

Comparing compound interest (fv) with Present value (pv)

19-22Slide23

Problem 19-11

Solution:8 years x 2 = 16 periods 6% 2

= 3%

$

40,000 x (1 = .03)

16

=

$

64,188.26

19-

23

Lynn Ally, owner of a local Subway shop, loaned $40,000 to Pete Hall to help him open a Subway franchise. Pete plans to repay Lynn at the end of 8 years with 6% interest compounded semiannually. How much will Lynn receive at the end of 8 years?

LU 19-1(2)

Step 1: Input 16 and then press

N

.

Step 2: Input 6/2

=

and then press

I/Y

.

Step 3: Input 40,000

+/-

and then press

PV

.

Step 4: Input 0 and then press

PMT

.

Step 5: Press

CPT

FV

=

64,188.26.Slide24

Problem 19-13

Solution:Mystic4 years x 2 = 8 periods

10% 2

= 5%

FV = $10,000(1 + .05)

8

=

$

14,774.55

$14,774.55 - $10,000 =

$4,774.55

Four Rivers

4 years x 4 = 16 periods

8%

4

= 2%

FV = $10,000(1 +.02)

16

=

$13,727.86

$13,727.86 - $10,000 =

$3727.86

19-

24

Melvin Indecision has difficulty deciding whether to put his savings in Mystic Bank or Four Rivers Bank. Mystic offers 10% interest compounded semiannually. Four Rivers offers 8% interest compounded quarterly. Melvin has $10,000

to invest. He expects to withdraw the money at the end of 4 years. Which bank gives Melvin the better deal? Check your answer.

LU 19-1(2)Slide25

Problem 19-14

Solution: 3 years x 2 = 6 periods9% 2 = 4.5%

$59,533.90(1 + .045)6 = $77,528.62

19-

25

Lee Holmes deposited $15,000 in a new savings account at 9% interest compounded semiannually. At the beginning of year 4, Lee deposits an additional $40,000 at 9% interest compounded semiannually. At the end of 6 years, what is the balance in Lee’s account?

LU 19-1(2)

$15,000(1 + .045)

6

= $19,533.90

+ 40,000.00

$ 59,533.90Slide26

Problem 19-23

Solution:8 years x 2 = 16 periods6% 2

= 3%

$

6,000(1 + .03)

16

=

$3,739.00

19-

26

Paul Havlik promised his grandson Jamie that he would give him $6,000 8 years from today for graduating from high school. Assume money is worth 6% interest compounded semiannually. What is the present value of this $6,000?

LU 19-2(2)

Step 1: Input 16 and then press

N

.

Step 2: Input 6/2

=

and then press

I/Y

.

Step 3: Input 6000 and then press

FV

.

Step 4: Input 0 and then press

PMT

.

Step 5: Press

CPT

PV

=

-3739.00