applying financial formulas copyright 2014 scott storla

Copyright 2014 Scott Storla

Applying Financial Formulas


Vocabulary

Equation

Rate

Interest rate

Simple interest

Compound interest


A rate is an expression, often in the form of a fraction, which compares one quantity to another quantity.

For instance sixty miles per hour, , compares

an amount of distance to an amount of time.

An interest rate compares the price to borrow money to one year of time. An interest rate is expressed as a percent but we typically work with the rate as a decimal. If you invest in a bond that pays 3% then after one year you’ll earn three cents for every dollar you invested. On the other hand if your credit card has a rate of 18% then every year you’ll pay the credit card company eighteen cents for every dollar you’ve borrowed for one year.

60 miles1 hour


The formula for simple interest, helps find A, the future value of the account, after t years. P is the original amount invested or borrowed (the principal) and r is the annual interest rate written as a decimal.

A formula uses an equation to express a fact or rule. Usually the left hand side is a single letter that represents the concept we’re working with. The right hand side includes numbers, variables, operators and grouping symbols.

1 ,A P r t

An expression is a meaningful collection of numbers, letters, operations and the idea of grouping.

If two expressions are separated by the equality symbol, =, we have an equation.


Answer the questions using the

simple interest formula, 1 .A P r t

Find the value after 3 years if $1000 is deposited at a rate of 3% simple interest.

1A P r t

1,000 1 0.03 3A

1,000 1.09A

1,090A

$1,090


Answer the questions using the

simple interest formula, 1 .A P r t

1A P r t

10,000 1 0.015 30A

10,000 1.45A

14,500A

$14,500

How much is in an account that starts with $10,000 and earns 1.5% simple interest for 30 years?


A common formula for compound interest

is, The variables A, P, r and t have the same meaning as for simple interest and e is a constant whose value is approximately 2.718.

With compound interest accumulated interest is returned to the account as principal and begins to itself earn interest.

.rtA Pe


Evaluating with e

0.07 3 1.2337e

0.05 3100 116.18e

0.10 41000 670.32e


Using the Continuous Compounding Formula


Use the future value formula to answer the question.rtA Pe

Find the amount if $5,000 is compounded continuously for 3 years at 6.5%.

rtA Pe

0.065 35,000A e

0.1955,000A e

5,000 1.21531A

$6076.55

6076.55A


Imagine you were able to transport 200 years into the past and deposit $10 of money from the period into an account paying 6%. If one hour after making the deposit you were transported back to today, how much would be in the account?

rtA Pe

1210A e

$1,627,547.91

1627547.914A

0.06 20010A e



A bank pays 0.25% on money deposited and charges 7% to loan the same money to others. How much does the bank make per year for every $100 that it receives and then loans to others?

rtA Pe

$7

7.00051A

0.07 1 0.0025 1100 100A e e


107.25082 100.25031A


Present value is the amount we need to invest today to have a certain amount in the future.

By rewriting the future value formula we can build

the present value formula, rtP Ae


Use to find the present value.rtP Ae

In 20 years I would like to have $1,000,000 for my retirement. How much do I need today in an account that earns 6.2% to have $1,000,000 in 20 years?

rtP Ae

(0.062 20)1,000,000P e

1.241,000,000P e

1,000,000 0.2893842179P

289,385P

I would need $289,385.


Use to find the present value.rtP Ae

250 years from today you’d like to leave a distant relative a million dollars. If your account earns 5% how much should you set aside today?

rtP Ae

(0.05 250)1,000,000P e

12.51,000,000P e

3.7266...P

Set aside $3.73


lnSolving the future value formula for , ,

allows us to answer questions about the interest rate.

A Pr r

t


What interest rate is needed for $12,000 to become $18,000 in 7 years?

lnUse to find the interest rate.

AP

rt

18,000ln

12,0007

r

0.4054651

7r

0.0579235r

I’d want a rate of at least 5.8%?


What interest rate will double your $12,000 in 5 years?

lnUse to find the interest rate.

AP

rt

24,000ln

12,000

5r

0.138629r

I’d like to get at least 13.9%


1Solving the future value formula for , ln

allows us to answer questions about the time.

t t A P r


$5,000 is invested at 5%. When will the account have $8,000?

1Use ln to find the time.A

t rP

18,000ln 0.05

5,000t

10.47 0.05t

9.4t

A little under nine and a half years.


Compare the length of time it takes to double $1,000 at 10% interest versus 1% interest?

1Use ln to find the time.A

t rP

12000ln 0.1

1000t

12000

ln 0.011000

t

6.9t 69t

At 10% interest it takes a little under 7 years to double your money.

At 1% interest it takes a little over 69 years to double your money.


Applying Financial Formulas

applying financial formulas copyright 2014 scott storla

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