7.8 Simple and Compound Interest - Presentation Transcript

1. Chapter 7, Section 8: Simple and Compound Interest January 15 th , 2009 Total Real Life Stuff 2. Warm Up:

o Find 6% of $400.

o Find 5% of $2,000.

o Find 4.5% of $700.

o Find 5.5% of $325.

$24 $100 $31.50 $17.88

3. Simple Interest o When you first deposit money in a savings account, your deposit is called PRINCIPAL .

o The bank takes the money and invests it.

o In return, the bank pays you INTEREST based on the INTEREST RATE.

o Simple interest is interest paid only on the PRINCIPAL.

4. Simple Interest Formula

o I = prt

o I = interest

o P = principal

o R = the interest rate per year

o T = the time in years .

5. Real-World

o Suppose you deposit $400 in a savings account. The interest rate is 5% per year.

o Find the interest earned in 6 years. Find the total of principal plus interest.

o FormulaI = P R T

o P = 400 , R = 0.05 = 5% , T = 6 (in years)

o 400 x 0.05 = 20 = interest on one year

o 400 x 0.05 x 6 = 120 = interest on $400 over 6 years

o 400 + 120 = $520 = amount in account after 6 years.

6. Now Figure Interest In Months

o Remember that T = time in Years .

o So, Find the interest earned in three months. Find the total of principal plus interest.

o What fraction of a year is 3 months ?

o T = 3/12 = ¼ or 0.25

o I = PRT

o I = 400 x 0.05 x 0.25

o I = $5 = interest earned after 3 months

o $5 + $400 = total amount in account

o $405

7. Try These: Both Find the Simple Interest

o Principal = $250

o Interest Rate = 4%

o Time = 3 Years

o Principal = $250

o Interest Rate = 3.5%

o 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. $30 $4.38

8. Compound Interest o Compound Interest is when the bank pays interest on the Principal AND the Interest

already earned.

o The Balance is the Principal PLUS the Interest.

o The Balance becomes the Principal on which the bank figures the next interest payment when doing Compound Interest.

9. Compound Interest Example

o 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. Fill In This Chart $486.20 Year 4: Year 3: Year 2: Year 1: $400.00 Balance at End of Each Year Interest (I = PRT) Principle @ Beginning of Year

11. Compound Interest Formula

o You can find a balance using compound interest in one step with the compound interest formula.

o An INTEREST PERIOD is the length of time over which interest is calculated.

o The Interest Period can be a year or less than a year.

12. Compound Interest Formula

o B = p(1 + r) n

o B = the final balance

o P = is the principal

o R = the interest rate for each interest period

o N = the number of interest periods.

13. Semi-Annual

o 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. Example o Find the balance on a deposit of $1,000, earning 6% interest compounded semiannually

for 5 years.

o 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.

o Now plug it into the formula!

15. The Formula!

o B = p (1 + R) n

o B = $1,000 (1 + 0.03) 10

o B = $1,000 (1.03) 10

o B = $1,000 (1.34391638)

o B = $1,343.92

o Happy? You’ll actually get to use a calculator for these =]

16. Try These: Both

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

o Compounding Annually

o Compounding Semiannually

$955.09 $955.37