Compound interest

The interest earned is periodically added to the principle and hence both the original principal and the interest earned earn interest at the same rate. Compound interest increases exponentially over time.
Compound

Formula 

F = P(1 + i)n (future value)
P = F(1 + i)-n (present value)
where 
P = principal
F = future value OR accumulated amount
r = annual interest rate (a.p.r.)
m = number of compounding periods per year
t = time in years
     r
i =     = interest rate per compounding period
     m
n = m t = total number of compounding periods
Example:     Suppose $1,000 is deposited in an account earning compound interest at
an annual rate of 8%. Compute the amount of money accumulated in 10 years
if the interest is
a) compounded annually
b) compounded quarterly
c) compounded daily 
Compounded annually
     r    0.08    
i =     =      = 0.08   n = mt = 1(10) = 10
     m     1
F = P(1 + i)n = $1,000(1 + 0.08)10 = $2,158.92
Compounded quarterly
     r    0.08    
i =     =      = 0.02   n = mt = 4(10) = 40
     m     4
F = P(1 + i)n = $1,000(1 + 0.02)40 = $2,208.04
Compounded daily
The daily ionterest is very small and the calculation is 
very sensitive to roundoff errors.  I recommend using as 
many digits as you calculator allows.
     r    0.08    
i =     =      = 0.00219178082
     m    365
n = mt = 365(10) = 3650
F = P(1 + i)n = $1,000(1 + 0.00219178082)3650 = $2,225.35
Example:     Suppose some money is deposited in an account earning compound interest
at an annual rate of 8% compounded quarterly. How much money must
be invested now in order to accumulate $1,000 in 10 years ? 
     r    0.08    
i =     =      = 0.02   n = mt = 4(10) = 40
     m     4
P = F(1 + i)-n = $1,000(1 + 0.02)-40 = $452.89

Exercises 


(1) Find the amount of money accumulated if $10,000 is deposited 
    in an account paying an annual interest rate of 6% compounded
    quarterly for 10 years.
     $16,000.00
     $17,908.48
     $18,140.18
     $18,221.19 


(2) Find the present value of $10,000 due in 10 years invested
    at an annual interest rate of 6% compounded quarterly. 
     $5,488.12 
     $5,512.62
     $5,583.95
     $6,250.00


(3) A family is planning to purchase a home 5 years from now.
    If the cost of the home increases at a rate of 6% per year
    during this period, how much will the family pay for a home
    that currently costs $100,000. 
     $130,000.00
     $133,822.55
     $134,985.88

Calculator

Amount
Annual interest rate as a decimal
Number of compounding periods per year
Length of the investment in years



Future value
Present value

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