# Lesson 7.8

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Education

Published on February 11, 2009

Author: rdtowsley

Source: slideshare.net

Simple and Compound Interest J8

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 - interest paid only on the PRINCIPAL.

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 - interest paid only on the PRINCIPAL.

Ex. 1 Simple Interest Formula I = prt I = interest P = principal R = the interest rate per year T = the time in years .

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. a. Find the interest earned in 6 years. Find the total of principal plus interest. I = P R T  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.

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

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

I = P R T  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.

b. Now Figure Interest In Months Remember that T = time in Years . 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

Remember that T = time in Years .

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

Now you try! Find the Simple Interest 1. Principal = \$250 Interest Rate = 4% Time = 3 Years 2. 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. \$30 \$4.38 I = PRT

1.

Principal = \$250

Interest Rate = 4%

Time = 3 Years

2.

Principal = \$250

Interest Rate = 3.5%

Time = 6 Months

Ex. 2 Compound Interest Compound Interest - when the bank pays interest on the Principal AND the Interest already earned. Balance - the Principal PLUS the Interest. The Balance becomes the Principal on which the bank figures the next interest payment when doing Compound Interest.

Compound Interest - when the bank pays interest on the Principal AND the Interest already earned.

Balance - the Principal PLUS the Interest.

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

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.

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.

Fill In This Chart \$486.20 Year 4: Year 3: 420.00 Year 2: 400 + 20 = 420.00 400.00 · 0.05 = 20.00 Year 1: \$400.00 Balance at End of Each Year Interest (I = PRT) Principle @ Beginning of Year

Compound Interest Formula You can find a balance using compound interest in one step with the compound interest formula. INTEREST PERIOD - the length of time over which interest is calculated. The Interest Period can be a year or less than a year.

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

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

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

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.

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.

Ex. 3 Semi-Annual When interest 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 payment periods = number of years x number of interest periods per year.

When interest is compounded semiannually (twice per year), you must DIVIDE the interest rate by the number of interest periods, which is 2.

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!

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!

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

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

Now you try! Find the balance for each account. Amount Deposited: \$900, Annual Interest Rate: 2%, Time: 3 Years. 3. Compounding Annually 4. Compounding Semiannually \$955.09 \$955.37

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

3. Compounding Annually

4. Compounding Semiannually

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August 19, 2017

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August 19, 2017

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