Mathematics: MATH650 section 02
Wendy Forbes
April 27, 2010

We often hear people say that we should let our money work for us. Using money or capital for income or profit is called an investment.

An accountant manages a company’s money. Then, managers or company investors review their reports to find out the financial status. The demand for accountants increases as more private companies are established. In addition, there are always new and changing laws that increase the need for a person with these skills.

Continuously Compounded interest is what banks normally use to calculate the interest on investments. This method is the equal of continually recalculating the interest based on the current principal amount.

There are different types of Compound Interest. Interest is the amount of money earned in a saving account. * Simple Interest: Interest calculated once on the principal. * Compound Interest: Interest calculated for a given segment of time of the investment. For example, compounded monthly, means the interest is calculated each month and combined with the principal. So, for the next month, interest is earned on the interest.

Continuously Compound Interest Formula

P: ending principal
P0: initial principal
e: constant e
k: interest
t: time as measured in years

Example problem:
Let’s say your accountant invests $5,000.00 in a saving account at a bank for you that earns 5% interest compounded continuously. How would we know what is earned after 10 years?

We start with our formula.

* We determine the values for each of the variables in the formula: * P0 = $5000.00Initial principal
* k = 5% but use the decimal equivalent 0.05
* t = 10Number of years
* e is a special number used to get the natural exponential growth. It is used throughout math and is approximately 2.7183.
Also, it is usually...

... because
log(0.1) = -1
log(1) = 0
log(100) = 2
log(1000) = 3
So the graph will be much easier to read.
Logarithms are used in a lot of places to scale numbers when there's a big range between the smallest and the largest numbers of interest, which makes them easier to talk about.
y=yi x e^-kt
where:
y - different between temprature of body and the constant temp of room
yi - initial temprature difference of body and room
e - eulers number (2.718...)
t -...

...commencing at age 60 and ending at age 67
Plan 1:
V0 * (1.06)42 = 3,000,000
V0 = 3,000,000/(1.06)42
V0 = $259,582.20
Plan 2:
V0 * (1.06)17 = 3,000,000
V0 = 3,000,000/(1.06)17
V0 = $1,114,093.26
Plan 3:
C * Annuity Compound Factor (6%, 37) = 3,000,000
C * [((1.06)37 – 1)/0.06] = 3,000,000
C *127.27 = 3,000,000
C = $23,572.28
Plan 4:
C * Annuity Compounding Factor (6%,17) = 3,000,000
C * 28.21 = 3,000,000
C = $106,334.41...

...13.1 CompoundInterest
• Simple interest – interest is paid only on the
principal
• Compoundinterest – interest is paid on both
principal and interest, compounded at regular
intervals
• Example: a $1000 principal paying 10% simple
interest after 3 years pays .1 3 $1000 = $300
If interest is compounded annually, it pays .1
$1000 = $100 the first...

...Chapter 5 : Interet rates
Page161
Interest rate quotes and adjustments
5-1. Your bank is offering you an account that will pay 20% interest in total for a two-year deposit. Determine the equivalent discount rate for a period length of
a. Six months.
b. One year.
c. One month.
a. Since 6 months is [pic] of 2 years, using our rule [pic]
So the equivalent 6 month rate is 4.66%.
b. Since one year is half of 2 years [pic]
So the equivalent...

...year. The firm net fixed assets of $161,900. What is the amount of the net working capital?
3. Kaylor Equipment Rental paid $75 in dividends and $511 in interest expense. The addition to retained earnings is $418 and net new equity is $500. The tax rate is 35 percent. Sales are $15,900 and depreciation is $680. What are the earnings before interest and taxes?
4. The Widget Co. purchased new machinery three years ago for $4 million. The machinery can be sold to...

...COMPOUNDINTEREST
Making or Spending Money
SIMPLE INTEREST FORMULA
If a principal of P dollars is borrowed for a
period of t years at a per annum interest rate
r, expressed as a decimal, then interest I
charged is
I Pr t
This interest is not used very often. Interest is
usually compounded which means interest
is charged or given on the interest and the...

...your
objectives? Assume interest remains at 9%. [Rs.1254]
2. You can deposit Rs.4000 per year into an account that pays 12% interest. If you
deposit such amounts for 15 years and start drawing money out of the account in
equal annual installments, how much could you draw out each year for 20 years?
[Rs.19964.12]
3. What is the value of a Rs.100 perpetuity if interest is 7%? [Rs.1428.57]
4. You deposit Rs.13,000 at the beginning of every year...

...A) B) Answer C) D)
1. What is the simple interest for a principal of $620 invested at a rate of 7% for 3 years? $173.60 $130.20 $172.60 $129.20
A) B) C) Answer D) E)
2. If you borrow $1100 for 5 years at 14% annual simple interest, how much must you repay at the end of the 5 years? $770.00 $2215.13 $2117.96 $77,000 $1870.00
A)Answer B) C) D)
3. How much interest is earned in 5 years on $2,900 deposited in an account paying 7.1%...

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