explain the difference between simple interest and compound interest

Answer 1

simple interest = interest only on the principal

compound interest = interest on the principle + interest on the interest

I = Port = simple interest = Principal time annual rate of interest times years

P = Poe^rt is the general formula for compound interest, compounded continuously

P-Po =the interest when compounded or when not compounded

P = Po(1 + r/n)^nt is the general formula for compound interest where n = the number of compounding periods per year. as n approaches infinity the formula collapses to P = Poe^rt

for example, simple interest on $1,000 at 4% for 2 years =1000(.04)(2) = $80

P - Po = 1080-1000 = $80

continuously compounded interest on $1,000 at 4% for 2 years

= P - Po where P = Poe^.04(2) = 1000e^.08 = about $1083.29

P-Po = 1083.29 -1000 = $83.29 which = simple interest + interest on the interest = $80 +$3.29

Answer 2

In simple interest transactions the interest is earned ONLY on the principal no matter how long the period;

Interest = Principle * Rate * Time.

In compound interest transactions, interest is earned on both the principal AND any accrued interest;

Amount = Principal * (1 + annual rate)ⁿ where n is the number of years in the transaction.