Compound Interest

Essential Skill: Demonstrate Understanding of Concept

Compound InterestInterest compounded annually means you find the interest after one year and add it to your principal

In the second year, the interest becomes part of the principal

Continue with this method for the amount of time you invest

What is the difference between simple and compound interest?

Simple Interest: Interest that is earned or paid only on the principal.

Compound Interest

Simple Interest: You deposit $50 in a saving account that earns 2% interest. After 3 years how much money is in the account?

I=Prt  

Compound Interest: You deposit $50 in a savings account that earns 2% interest annually. After 3 years how much money is in the account?

How could we find the balance at the end of each year without adding?

 Multiply by 1.02

Compound Interest: You deposit $50 in a savings account that earns 2% interest annually. After 3 years how much money is in the account?

Try the same problem this way:

Compound Interest: You deposit $50 in a savings account that earns 2% interest annually. After 3 years how much money is in the account? 

 Principal at start of year  Balance at end of year

Year 1 $50  A= 50(1+.02) A = $51

Year 2 $51  A = 51(1+.02) A = $52.02

Year 3 $52.02  A = 52.02(1 + .02) A = $53.06

Here is another way to look at the problem:

Compound Interest

When an account earns interest compounded annually, the balance A is given by the formula:

A = P(1 + r)t

Where P is the principal, r is the annual interest rate (written as a decimal), and t is the time in years.

1.) You deposit $1,500 into an account that earns 2.4% interest compounded annually. Find the balance after 6 years.

Find the balance using both simple and compound interest for the following:

2.) Simple CompoundP = $10,000 P = $10,000r = 8.5% r = 8.5% compounded annuallyt = 3 years t = 3 years

Find both simple and compound interest for the following:

3.) Simple CompoundP = $500 P = $500r = 4.25% r = 4.25% compounded annuallyt = 25 years t = 25 years

Find both simple and compound interest for the following:

4.) Simple CompoundP = $1,250 P = $1,250r = 2% r = 2% compounded annuallyt = 5 years t = 5 years

Challenge

What is the account compounds on a time frame shorter than a year?A = P (1 + )nt

where P = Principal, r = interest rate, t = time in years, and n = number of times per year interest is compounded

You deposit $1000 into an account that earns 6% interest compounded semiannually. What is the balance after 4 years?

r

n

P = $3000, r = 6.2%, t = 7 years, compounded quarterly

P = $500, r = 4%, t = 8 years, compounded monthly