Simple and
Compound
Interest
Warm Up:
 Find

6% of $400.

 Find

5% of $2,000.

 Find

4.5% of $700.

 Find

5.5% of $325.
Simple Interest
 When

you first deposit money in a savings
account, your deposit is called PRINCIPAL.
 The bank takes t...
Simple Interest Formula
I = prt
I

= interest
P = principal
R = the interest rate per year
T = the time in years.
Real-World
 Suppose

you deposit $400 in a savings account.
The interest rate is 5% per year.
 Find the interest earned ...
Now Figure Interest In Months
 Remember

that T = time in Years.
 So, Find the interest earned in three months.
Find the...
Try These: Both
Find the Simple Interest
 Principal

= $250
 Interest Rate = 4%
 Time = 3 Years
 Principal

= $250
 I...
Compound Interest
 Compound

Interest is when the bank pays
interest on the Principal AND the Interest already
earned.
 ...
Compound Interest Example
 You

deposit $400 in an account that earns 5%
interest compounded annually (once per year).
Wh...
Fill In This Chart
Principle @
Beginning of
Year
Year 1:
$400.00
Year 2:
Year 3:
Year 4:

Interest
(I = PRT)

Balance at E...
Compound Interest Formula
 You

can find a balance using compound
interest in one step with the compound
interest formula...
Compound Interest Formula
B = p(1 + r)n
B = the final balance
P = is the principal
R = the interest rate for each interest...
Semi-Annual
 When

interested is compounded semiannually
(twice per year), you must DIVIDE the interest
rate by the numbe...
Example
 Find

the balance on a deposit of $1,000, earning
6% interest compounded semiannually for 5
years.
 The interes...
The Formula!
B = p (1 + R)n
B = $1,000 (1 + 0.03)10
B = $1,000 (1.03)10
B = $1,000 (1.34391638)
B = $1,343.92
Happy? You’l...
Try These: Both
 Find

the balance for each account. Amount
Deposited: $900, Annual Interest Rate: 2%, Time:
3 Years.

 ...
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Simple and compound interest student

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Simple and compound interest student

  1. 1. Simple and Compound Interest
  2. 2. Warm Up:  Find 6% of $400.  Find 5% of $2,000.  Find 4.5% of $700.  Find 5.5% of $325.
  3. 3. Simple Interest  When you first deposit money in a savings account, your deposit is called PRINCIPAL.  The bank takes the money and invests it.  In return, the bank pays you INTEREST based on the INTEREST RATE.  Simple interest is interest paid only on the PRINCIPAL.
  4. 4. Simple Interest Formula I = prt I = interest P = principal R = the interest rate per year T = the time in years.
  5. 5. Real-World  Suppose you deposit $400 in a savings account. The interest rate is 5% per year.  Find the interest earned in 6 years. Find the total of principal plus interest.  I = PRT  Formula  P = 400, R = 0.05 = 5%, T = 6 (in years)  400 x 0.05 = 20 = interest on one year  400 x 0.05 x 6 = 120 = interest on $400 over 6 years  400 + 120 = $520 = amount in account after 6 years.
  6. 6. Now Figure Interest In Months  Remember that T = time in Years.  So, Find the interest earned in three months. Find the total of principal plus interest.  What fraction of a year is 3 months? T = 3/12 = ¼ or 0.25 I = PRT I = 400 x 0.05 x 0.25 I = $5 = interest earned after 3 months $5 + $400 = total amount in account $405
  7. 7. Try These: Both Find the Simple Interest  Principal = $250  Interest Rate = 4%  Time = 3 Years  Principal = $250  Interest Rate = 3.5%  Time = 6 Months Reminder: Time is always in terms of Years. So, if you’re dealing with months, you have to make your months a fraction of a year.
  8. 8. Compound Interest  Compound Interest is when the bank pays interest on the Principal AND the Interest already earned.  The Balance is the Principal PLUS the Interest.  The Balance becomes the Principal on which the bank figures the next interest payment when doing Compound Interest.
  9. 9. Compound Interest Example  You deposit $400 in an account that earns 5% interest compounded annually (once per year). What is the balance in your account after 4 years? In your last calculation, round to the nearest cent.
  10. 10. Fill In This Chart Principle @ Beginning of Year Year 1: $400.00 Year 2: Year 3: Year 4: Interest (I = PRT) Balance at End of Each Year
  11. 11. Compound Interest Formula  You can find a balance using compound interest in one step with the compound interest formula.  An INTEREST PERIOD is the length of time over which interest is calculated.  The Interest Period can be a year or less than a year.
  12. 12. Compound Interest Formula B = p(1 + r)n B = the final balance P = is the principal R = the interest rate for each interest period N = the number of interest periods.
  13. 13. Semi-Annual  When interested is compounded semiannually (twice per year), you must DIVIDE the interest rate by the number of interest periods, which is 2. 6% annual interest rate 2 interest periods = 3% semiannual interest rate To find the number of payment periods, multiply the number of years by the number of interest periods per year.
  14. 14. Example  Find the balance on a deposit of $1,000, earning 6% interest compounded semiannually for 5 years.  The interest rate R for compounding semiannually is 0.06 2, or 0.03. The number of payment periods N is 5 years x 2 interest periods per year, or 10.  Now plug it into the formula!
  15. 15. The Formula! B = p (1 + R)n B = $1,000 (1 + 0.03)10 B = $1,000 (1.03)10 B = $1,000 (1.34391638) B = $1,343.92 Happy? You’ll actually get to use a calculator for these =]
  16. 16. Try These: Both  Find the balance for each account. Amount Deposited: $900, Annual Interest Rate: 2%, Time: 3 Years.  Compounding Annually  Compounding Semiannually
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