Simple and Compound Interest

 Money earned/charged from an investment/loan  Calculated with a rate (proportion of the principal amount)  Banks pay you interest for your investment  you pay banks interest for loans What is interest?

 With simple interest, the interest is calculated at the end of the year (interest rates are given as an annual rate usually) on the original principal  Next year the interest is calculated again on the principal  Essentially the interest earned is the same each year  In real life, simple interest is not practical as it results in a loss for businesses Simple Interest

 The formula to calculate simple interest is: I=Prt  P= principal (original amount of loan or investment)  I= Interest (the value of interest at the end of the time period)  R= rate (the rate of the interest, on an annual basis, always convert from percent to decimal when calculating with formula)  T= time (years usually, sometimes it will have to be converted according to the situation) Calculating Simple Interest

 The formula to calculate the total value “amount” of the interest and the principal value the formula is” A= P+I  A= total amount  P= principal value  I= Interest value Calculating Simple Interest

 What would the value of a $4000 investment be after 7 years with interest at a rate of3%?  I=Prt  I=4000* 0.03* 7  I=840  A=P+I  A=  A=4840  The value of the investment after 7 years will be 4840 Example

 What would the value of a $5000 investment be after 16 months with interest at a rate of 3.9%  I=Prt  I=5000* 0.039* (16/12)  since a year is 12 months  I= 260  A=P+I  A=  A=5260  So the value of the investment after 16 months would be $5260 Example

 What would the value of a $500 investment be after 8 years if invested at a rate of 4.8%  Remember to calculate the total amount, not just the interest  Your answer should be $692 Practice!

 How much would you owe the bank if you took a loan of $7000 at a rate of 9% for 28 months?  Remember to convert the “time” unit into years  You should have an answer of $8470 Practice!

 Compound interest is when the interest calculated is calculated on the principal amount and the interest added from the previous term  This is a more commonly seen form of interest in the real world  It is also more profitable for investments as the interest value is calculated on a larger sum Compound Interest

The formula to calculate the value of compound interest is: I= Interest P=principal amount R= rate T= time for 1 compound period N= number of compound periods Calculating Compound Interest

 Compound interest can be calculated for different time period as well, not just annually Calculating Compound Interest TermMeaning AnnuallyOnce a year Semi-annuallyTwice a year Quarterly4 times a year (3 months in each quarter) Monthly12 times a year Weekly52 times a year Daily365 times a year

 What would the value of a $2000 bond be after 3 months at an interest rate of 5%  I= 2000 ( * 1/12)^3 (the months are converted as 1/12 as there are 12 months in a year, but to calculate for three months the exponent value is raised to 3)  A= Example

 How much would you owe the bank for a loan of $4000 compounded semi-annually for 4 years at an interest rate of 7%?  A= 4000* ( * ½)^8  semi annually makes the denominator for “time” 2 as it is calculated twice a year, whereas the exponent becomes 8 since in 4 years, if calculated twice each year the interest would be compounded 8 time  A= Example

 $2500 compounded quarterly for 5 years at a rate of 4.75%  Remember to convert the “time” unit  You should get $ as your answer Practice!

  Resources