Exercise Write 5% as a decimal. 0.05

Write 6.5% as a decimal Exercise

What fraction of a year is 9 months? Exercise

What fraction of a year is 8 months? Exercise

3,000(0.045)( ) Exercise

4( ) Exercise

Simple Interest Formula I = P r t, where I = interest, P = principal, r = annual rate of interest, and t = time in years.

Find the simple interest earned from a one-time investment of $3,000 at 8% interest if the account is closed at the end of 2 years. I = Prt = $480 Example 1 = 3,000(0.08)(2)

Aaron borrowed $465 for 1 year. His bank gave him a simple interest loan at 12% annual interest for 1 year. How much interest will he pay? I = Prt Aaron owes $55.80 simple interest on this loan. Example 2 = 465(0.12)(1) = 55.80

How much interest is owed at the end of two years on a loan of $500 at 9% simple interest? $90 Example

Amount Formula A = P + I, where A = amount due, P = principal, and I = interest.

Find the interest and the total value of an investment of $1,500 at 5% simple interest for 9 months. t = 9 12 == = 0.75 I = Prt A = P + I = $1, Example 3 = 1,500(.05)(.75) = = 1,

What is the total amount owed at the end of two years on a loan of $500 at 9% simple interest? $590 Example

Compound interest – money paid on both the principal and previous interest earned

Interval annually Meaning # # semiannually quarterly monthly every year every six months every three months every month

4,000(0.03)(1) = $120 4,000(0.03)(0.25) = $30 4, = $4,030 4,030(0.30)(0.25) = $ , = $4,060.23

4,060.23(0.03)(0.25) = $ , = $4, ,090.68(0.30)(0.25) = $ , = $4, , – 4,000 = $121.36

A savings account offers 4% interest compounded monthly. Find the amount in the account at the end of 3 mo. if the initial deposit is $10,000. How much interest was earned during the first 3 mo.? Example 4

Since the interest is computed monthly, let t = Use a calculator to multiply the principal times 0.04; then divide the product by 12. Remember to round to the nearest cent.

Period Principal Interest New Principal $10,000 = $10, ≈ $ , ,000(.04)( ) 1 12

Period Principal Interest New Principal $10, = $10, ≈ $ , ,033.33(.04)( ) 1 12

Period Principal Interest New Principal $10, = $10, ≈ $ , ,066.77(.04)( ) 1 12

The amount of interest earned was 10, – 10,000 = $

An investment pays 8% interest compounded annually. How much interest is paid on a deposit of $1,000 left in for two years? $ Example

How much interest would that same $1,000 earn in two years at 8% if simple interest was used? $160 Example

Annual Compound Interest Formula S = P(1 + i) n, where S = amount in the savings account, P = principal, i = annual interest rate, and n = number of annual interest payments.

Use a calculator to find the amount in a savings account at the end of 5 yr. if $5,200 is invested at 3.5% interest compounded annually. Also, find the amount of interest earned. Example 5

P = $5,200i = 3.5% = 0.035n = 5 S = P(1 + i) n S = 5,200( ) 5 S = 5,200(1.035) 5 S = 5,200( ) S = $6, , – 5,200= $975.97

What is the interest earned on $1,000 at 8% over a time period of twenty years compounded annually? What is the simple interest earned over twenty years? $3,660.96; $1,600 Example

What would the interest be on $1,000 over a twenty-year period at 8% compounded quarterly? $3, Example