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