Lecture Practical business math procedures (11/e) - Chapter 12: Compound interest and present value

After reading the material in this chapter, you should be able to: Compare simple interest with compound interest, calculate the compound amount and interest manually and by table lookup, explain and compute the effective rate (APY), compare present value (PV) with compound interest (FV), compute present value by table lookup, check the present value answer by compounding.

Chapter Twelve

Compound Interest and

Present Value

Copyright © 2014 by The McGraw­Hill Companies, Inc. All rights reserved McGraw­Hill/Irwin

1. Compare simple interest with compound interest.

2. Calculate the compound amount and interest manually and by

table lookup

3. Explain and compute the effective rate (APY)

LU 12-1 Compound Interest (Future Value) – The Big Picture

Learning unit objectives

LU 12-2 Present Value The Big Picture

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

2. Compute present value by table lookup

3. Check the present value answer by compounding

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

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

Future Value of $1 at 8% for Four Periods

(Figure 12.1)Manual Calculation

1.00

$ $ 1.08 $ 1.17 $ 1.26

0.08

0.08 0.08 0.08Interest $ 0.08 $ 0.09 $ 0.09 $ 0.10

Beg Bal 1.00 1.08 1.17 1.26

End of year $ 1.08 $ 1.17 $ 1.26 $ 1.36

Tools for Calculating Compound Interest

Number of periods (N)

Number of years multiplied by

the number of times the

interest is compounded per

year

Rate for each period (R) Annual interest rate divided by the number of times the interest is compounded per

year

If you compounded $100 for 4 years at 8% annually,

semiannually, or quarterly, what is N and R?

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

Calculating Compound Amount

by Table Lookup

Step 1 Find the periods: Years multiplied by number of times

interest is compounded in 1 year

Step 2 Find the rate: Annual rate divided by number of times

interest is compounded in 1 year

Step 3 Go down the period column of the table to the number

desired; look across the row to find the rate At the

intersection is the table factor for the compound amount of

$1

Step 4 Multiply the table factor by the amount of the loan This

gives the compound amount

Future Value of $1 at Compound Interest

Calculating Compound Amount

by Table Lookup

Pam Donahue deposits $8,000 in her savings account that pays 6%

interest compounded quarterly What will be the balance of her

account at the end of 5 years?

Nominal and Effective Rates (APY) of

Nominal Rate (stated rate) –

The rate on which the bank calculates interest

Calculating Effective Rate APY

Nominal and Effective Rates (APY) of

Interest Compared (Figure 12.3)

Compounding Interest Daily

Use Table 12.2 to calculate what $1,500 compounded daily for

5 years will grow to at 7%

N = 5

R = 7%

Factor, 1.4190

$1,500 x 1.4190 = $2,128.50

Present Value of $1 at 8% for Four Periods (Figure 12.4)

Number of periods

Present value goes from the future value to the present

value

Present value

$1.0000

Future Value

Calculating Present Value by

Table Lookup

Step 1 Find the periods: Years multiplied by number of times

interest is compounded in 1 year

Step 2 Find the rate: Annual rate divided by number of times

interest is compounded in 1 year

Step 3 Go down the Period column of the table to the number

desired; look across the row to find the rate At the

intersection of the two columns is the table factor for the

compound value of $1

Step 4 Multiply the table factor by the future value This is

the present value

Comparing Compound Interest (FV)

(Table 12.1) with Present Value (PV) (Table 12.3)

Compound value Table 12.1

Table Present Future

amount and find

what the dollar

amount is worth in

the future

We know the future dollar amount and find what the dollar amount is worth in the present

Present value Table 12.3

Table Future Present 12.3 Value Value

.7350 x $108.84 =

$80.00 (N = 4, R = 8%)

Calculating Present Value Amount

by Table Lookup

Rene Weaver needs $20,000 for college in 4 years She can earn 8%

compounded quarterly at her bank How much must Rene deposit at the

beginning of the year to have $20,000 in 4 years?