Compound Interest

Compound Interest is interest that is computed on the principal and any accumulated interest.

Assume I had $1000, deposited in the bank for 3 years at 4% interest.

How much money would I have after 3 years

i = prt
p = $1,000
r = 4%
t = 3 years
     i = prt
     i = 1,000 × 0.04 × 3 = $120
     A = p + i 
     A = 1,000 + 120 = $1,120

What if I pulled the money out and reinvested it once a year

Year 1
    i = prt
    p = $1,000
    r = 4%
    t = 1 year
            i = prt 
	    i = 1,000 × 0.04 × 1  = $40
	    A = p + i
	    A = 1,000 + 40 = $1,040
Year 2
    i = prt
    p = $1040
    r = 4%
    t = 1 year
            i = prt 
	    i = 1,040 × 0.04 × 1  = $41.60
	    A = p + i
	    A = 1,040 + 41.60 = $1,081.60
Year 3
    i = prt
    p = $1081.60
    r = 4%
    t = 1 year
            i = prt 
	    i = 1,081.60 × 0.04 × 1  = $43.64
	    A = p + i
	    A = 1,081.60 + 43.64  = $1,124.86

Where did the extra $4.86 come from?

The compound interest formula
$A=p(1+{r \over n})^{nt}$
- A is the total amount
- p is the principal
- r is the compound interest rate
- n is the number of compounding periods per year
- t is the total number of years.
Let's do the same computation

A = p(1+r/n)^(nt)
    p = $1,000
    r = 4%
    n = 1
    t = 3 years

    A = p(1+r/n)^(nt)
      = 1000 (1+0.04/1)^(1*3) 
      = 1,124.86

      On my calculator
      1000 × ( 1 + .04/1) ^ ( 1 × 3)

Please figure out how to enter this on your calculator.
Do some problems 7-14
Sometimes this is called the future value
Sometimes we want to know how much money to invest now to have a determined amount in the future.
This is called the present value
$p={A \over (1+{r \over n})^(nt)}$
Do some problems 15-18
Do some problems 19 - 28
If time, Effective Annual Yield is the interest rate that corresponds to a simple interest loan.
- Just use p =1, t = 1 and compute
- This gives the equivalent Annual Percent Yield.
- Banks are required to give the APY for all loans.