259 Lecture 2 Spring 2013
Finance Applications with Excel –
Simple and Compound Interest
Finance Applications
 Excel is a useful tool for working with
financial applications that arise in
areas such as business, economics, or
actuarial science, including:
 Simple Interest
 Compound Interest
 Annuities
 Amortization
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Simple Interest
 In order to borrow (invest) money
from a bank, we have to pay (are
paid) interest on the money, which is
usually a percentage of the amount
borrowed (invested).
 Simple interest is a type of interest
that is paid only on the amount
borrowed (invested).
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Simple Interest (cont.)
 If we deposit P dollars at an annual
interest rate of r%, for a time period t
years, then the future value or
maturity value of the principal P is
given by
 A = P(1+r*t).
 Note that the interest is given by
 I = P*r*t.
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Simple Interest (cont.)
 Example 1: For which of the
following loans would we end up
paying less interest?
 (a) $10,000 borrowed for 1 year at
7% interest.
 (b) $9,000 borrowed for 11 months
at 8% interest.
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Simple Interest (cont.)
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Using Scenarios
 We can also use
Scenarios to
compare loans!
 Construct a “Simple
Interest Calculator”
in Excel!
 Click on the Data
tab and choose
What-If Analysis
from the Data Tools
group to pull up the
Scenario Manager.
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Using Scenarios (cont.)
 In the Scenario
Manager, choose
“Add” to add a new
scenario.
 Choose “Loan 1” as
the Scenario name and
choose cells B2:B4 as
the Changing cells.
 Change any cell values
you wish for the
scenario and click OK.
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Using Scenarios (cont.)
 Repeat the above
steps to add more
scenarios.
 Add a Scenario called
“Loan 2” with
appropriate data from
Example 1.
 Use 0.9167 or =11/12
for the time period
instead of 11/12.
(Why?)
 Choose “Summary” to
get a summary table
of all the scenarios!
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Using Scenarios (cont.)
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Present Value
 Suppose we wish to have a certain
amount of money at a future date,
based on money deposited today.
 The amount needed today is called
the present value of the future
amount.
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Present Value (cont.)
 If future amount A is obtained by
investing amount P today at simple
interest rate r% for t years, then
present value P can be found from
the future value formula above by
solving for principal P:
 P = A/(1+r*t)
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Present Value (cont.)
 Example 2: Tuition of $6000 will be
due when the spring semester starts
in 5 months.
 What amount should be deposited
today at 3% interest to have enough
to cover the tuition?
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Present Value (cont.)
 One way to solve this problem is to directly
calculate the present value of the $6000
using the formula P = A/(1+r*t).
 We find P = 6000/(1+0.03*(5/12)) =
5925.93 dollars.
 Another way is to guess choices for
principal P in the “Simple Interest
Calculator” we made in Excel until the
future value A is $6000.
 A third way is to use the Excel’s Goal Seek
tool, which attempts to solve problems with
one variable.
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Goal Seek
 Reset cell B2 to a
principal of 5000
dollars.
 Click on What-If
Analysis=>Goal
Seek.
 In the Goal Seek
dialog box, Set cell
B5, To value 6000,
By changing cell B2.
 Click OK and Excel
will try to find a
solution iteratively.
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Goal Seek (cont.)
 In this case, a solution
is found!
 Choose OK to keep the
solution, which is what
we calculated “by
hand” above!
 How about if we want
to have the entire
tuition payment in 4
months?
 Repeat with a time
period of 4 months to
get present value of
$5940.59.
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Goal Seek (cont.)
 Now, using the 4 month solution
we just found, try starting with an
interest rate of 8% and changing
the time period (via Goal Seek) to
get a future value of A = $6000.
 Note that Goal Seek requires a
value (i.e. number), not a formula
(such as =4/12) in the changing
cell.
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Compound Interest
 Simple interest is usually used for
loans or investments of one year or
less.
 For longer investment periods,
compound interest is used.
 In this case, interest is charged (paid)
on both interest and principal!
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Compound Interest (cont.)
 Suppose you put $10,000 into a bank
account earning 5% annual compound
interest.
 After 1 year, the account will have:
10,000 + 10,000*(0.05)=
10,000*(1+0.05) dollars
 After 2 years, the account will have:
10,000(1+0.05) + 10,000(1+0.05)*(0.05)
= 10,000*(1+0.05)2 dollars
 …
 After n years, the account will have:
10,000(1+0.05)n dollars.
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Compound Interest (cont.)
 In general, if P dollars are deposited for n
consecutive compounding periods at an
interest rate i per period, the compound
amount A is given by
 A = P(1+i)n.
 Note: As before for simple interest, we
also call P the principal or present value as
appropriate and call A the future value.
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Compound Interest (cont.)
 Example 3: Construct a table to compare the
difference between investing $10,000 at an
annual rate of 4% for 5 years with compound
interest and investments where the money is
compounded annually, quarterly, monthly,
daily, and hourly, and every minute!
 Which is the best investment?
 Is there much of a difference between the
last three investments?
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Compound Interest (cont.)
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Annuities and Amortization
 We’ll look at these next time!
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References
 Finite Mathematics and Calculus with
Applications (4th edition) by Margaret
L. Lial, Charles D. Miller, and
Raymond N. Greenwell
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