Sunday, June 16, 2013

Simple Interest vs. Compound Interest vs Continuously Compounded Interest

Simple Interest: You get some % of the original deposit. For example, if the original deposit is $1500, and the annual interest is 10%, then every year you will earn $150 from interest.

f(x)=$1500 +150x
f(1)=1500+150
f(2)=1500+150*2, etc.
f(8)=1500+150*8=1500+1200=2700

Compound Interest: You get some % both the original deposit plus the previously earned interest per pay period. For example, if the original deposit is $1500 and the the compound interest per month is 7.75%, then you earn 7.75% of $1500 + al previously earned interest.

f(x)=1500*(1+.0775)^x
f(1)=1500*1.0775=1616.25
f(2)=1500*1.0775^2=(1500*1.0775)*1.0775
=1616.25*1.0775=1741.5, etc.

f(8)=1500*(1.0775)^8=2725.39

Continuous Compound Interest Formula:
f(x)=Initial*e^(rate*time)
f(x)=1500*e^(.0775*t)
f(8)=1500*e^(.0775*8)=2788

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