The Difference Between Simple Interest and Compound Interest
We will be going into the difference between simple interest and compound interest. The results can be astounding when comparing the two results of any kind of example when comparing the two. To understand your finances and how your money works this will be a very integral part of knowledge.
The first and most important difference between these two types of interest is that in compound interest you begin to earn interest on the interest that you earned in the prior period. In simple interest this is not the case. In simple interest, which is used primarily in loans and short term periods, the principal is the only amount the interest is calculated from. In other words, you are going to accumulate a lot more interest when the interest is calculated by using compound interest.
When dealing with compound interest the interest is calculated on a daily, monthly, quarterly, semiannually, or annually. The formula that is used to calculate this interest on a bond for example would be Interest= Principal x Rate x Time (number of periods). By looking at this formula you can tell how the number of periods is going to be much different from how it looks in the simple interest formula.
When using simple interest the interest is calculated on a daily or monthly basis. The standard amount of days used in a calendar year is 360 rather than 365. The formula to calculate simple interest on a loan for example is also Interest= Principal x Rate x Time (a fraction such as 6/12).
As you can see by comparing the two formulas the difference between the “Time” portion of the formula is significantly different. By looking at this anyone can easily see why compound interest accumulates at such a higher rate than simple interest. Anyone who has any type of investments can easily see that they would much more prefer compound interest and people with loans would much more prefer simple interest.
...Jamie wants to earn $500 in interest so she’ll have enough to buy a used car. She puts $2000 into an account that earns interest. How long will she need to leave her money in the account to earn $500 in interest? 
  
Question #2 
  A local bank is advertising that you can double your money in eight years if you invest with them. Suppose you have $1000 to invest. What interest rate is the bank offering? 


Try These 
 
     
Question #1 
  Kelly plans to put her graduation money into an account and leave it there for 4 years while she goes to college. She receives $750 in graduation money that she puts it into an account that earns 4.25% interest. How much will be in Kelly’s account at the end of four years? 
 A. $127.50 
 B. $754.0425 
 C. $877.50 
 D. $1275 
    
Question #2 
  Randy wants to move his savings account to a new bank that pays a better interest rate of 3.5% so that he can earn $100 in interest faster than at his old bank. If he moves $800 to the new bank, how long will it take for him to earn the $100 in interest? 
 A. 3.57 years 
 B. 0.357 years 
 C. 0.28 years 

A father left a will of Rs.35 lakhs between his two daughters aged 8.5 and 16 such that they may get equal amounts when each of them reach the age...
...
If the principal is P50,000 and the interest rate is 12% compounded quarterly, what is the compound interest at the end of 5 years?
Find the compound amount if P17,500 is invested at 9.2% compounded semiannually for 3.5 years.
Determine the present value of P150,000 due in 6 years if the interest rate is 5.5% compounded annually.
If P135,650 is the maturity value of a sum invested at 13.2% compounded semiannually or 9 years and 6 months, find the present value and the compound interest earned.
For P97,500 to grow to P216,000 in 14 years, at what interest rate converted quarterly should it be invested?
A bond costs P279.50 and pays P356.25 five years later. At what rate compounded semiannually does it pay?
In how many months will a certain amount double itself if invested at 12% converted monthly?
How long will it take P40,000 to grow to P75,000 if it is invested at 24% compounded monthly?
What interest rate compounded quarterly is equivalent to 2.75% effective rate?
What nominal rate converted monthly is equivalent to 16% effective rate?
Which loan is better: 12.75% compounded semiannually or 12.5% compounded quarterly?
Two banks, A and B, are offering 2,5% (m=2) and 2.7% (m=1) respectively. If you are the investor, where would you prefer to put your money?
A noninterest bearing debt of P75,000 is due on May 1, 2005. If payment is deferred until May 1, 2007,...
...Q1: How long will it take for $20,000 to grow to $30,000 at 8%p.a. simpleinterest? (in years correct to two decimal places)
Q2: Calculate the present value of $10,000 due to be paid 3 years from now. The interest rate to use in the calculation is
i4 40%
Q3: Calculate the present value of $10,000 due to be paid 3 years from now. The interest rate to use in the calculation is
i2 40%
Q4: If compound interest is charged at 2.0% per month, what is the effective annual rate of interest (as a percentage correct to
two decimal places)?
Q5: How long (in years) does it take for money deposited in a bank account to accumulate to double the initial amount at the
interest rate
16%.
Q6: $10,000 is invested for 8 years. Calculate the future value if interest is at
years.
6% for 3 years followed by
12% for 5
Q7: A 180‐days promissory note (this is similar to a bank bill) will mature for $100,000 plus simpleinterest at 5%p.a. Calculate
the maturity value of the note. (Correct the answer to 2 decimal places.)
Q8: Seventy days after the issue date, the original owner sold the note to Tiffany for $97,651.13. Calculate the rate of simpleinterest p.a. used by Tiffany in calculating her purchase price. (The answer should be expressed as a percentage correct to 2 ...
...COMPOUND INTEREST
Making or Spending Money
SIMPLEINTEREST 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
principal.
SimpleInterest Example
COMPOUND INTEREST
Payment Periods:
Annually
Once per year
Semiannually
Twice per year
Quarterly
Four times per year
Monthly
Twelve times per year
Weekly
Fifty two times per year
Daily
365 (360 by banks) per year
COMPOUND INTEREST FORMULA
The amount A after t years due to a principal
P invested at an annual interest rate r
compounded n times per year is
r
A P 1
n
nt
A is commonly referred to as the
accumulated value or future value of the
account. P is called the present value.
COMPOUND INTEREST
Example:
Investing $1000 at an annual rate of 8%
compounded annually, quarterly, monthly,
and daily will yield the following amounts
after 1 year:
Annually
Quarterly
Monthly
Daily
COMPOUND INTEREST
Online example
More online examples
COMPOUND INTEREST
Tutorial
Continuous...
...Math 50
Solving SimpleInterest Problems using Systems of Equations
The simpleinterest I earned after one year on a deposit of principal P in an account earning interest at
an annual rate r is given by
(Notice that this is the Basic Percent Equation with percent r, base P and amount I.)
The problems below involve investing money in two different accounts, each paying annual simpleinterest at a different rate. For each problem, write one equation in two variables expressing a
relationship between the principals invested in the accounts, and another equation involving the
interest earned. Solve the system of the two equations then use the solution to answer the question.
Example: A total of $8000 is deposited in two simpleinterest accounts. One one account, the annual
simpleinterest rate is 5%, and on the second account, the annual simpleinterest rate is 6%. How much
should be invested in each account so that the total annual interest earned is $450?
Step 1: Use two variables to define two unknown quantities.
Let x represent the principal invested in the account paying 5% interest.
Let y represent the principal invested in the account paying 6% interest. ...
...savings account. Suppose you have a choice of keeping your money for five years in a savings account with a 2% interest rate, or in a five year certificate of deposit with and interest rate of 4.5%. Calculate how much interest you would earn with each option over five years time with continuous compounding.
I’m going to do this for my checking and savings account amount
Checking Account
A = Ce^RT My total money in the checking account is 2100 dollars Since the formula for the continuous compounding is A=Ce^RT where C is the initial deposit or capital, T for time, R is the rate of interest and A will be the final amount.
Capital = 2100, Interest Rate ( R) = 2% Time (T) = 5 years, e = 2.7182818284
When money kept for five years in a savings account with a 2% interest rate:
By using the values into formula:= 2100 e ^(0.02*5) = 2318.57
Interest earned = 2318.57 – 2100 = 218.57 dollars
Five year certificate of deposit with interest rate of 4.5%.So A = Ce^RT 2100e^4.5*5=2680.19  2100=$516.98
Savings Account = P*e^rt = Pe^(0.02*5) = Pe^0.1 = 1.105171P
Therefore, Interest = A  P = 0.105171P
Amount with certificate of deposit account = P*e^rt = Pe^(0.045*5) = Pe^0.225
= 1.252323P
Therefore, Interest = A  P = 0.252323P
A = 10,000e^(.02*5) = $11051.71 < 2%
A = 10,000e^(.045*5) = $12,523.23 <4.5%
(I would opt for...
...Compounded Interest
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.
* SimpleInterest: 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:...
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