# Math

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You deposit \$10,000 at 5% per year. What is the balance at the end of
one year if the interest paid is
(a) simple interest
(b) compounded monthly

• Math -

Let
A=amount at the end of n periods
r=interest rate per annum, 0.06 for 6% p.a.
R=interest rate per period, in the form
(1+r/k) where k=number of periods per year
(1+0.06)=1.06 for 6% p.a., or
(1+0.06/12)=1.005 for 6% p.a. compounded monthly

Simple interest:
A=PRn
=10000*1.05=10500

Compound interest:
A=PR^n
=10000*(1+0.05/12)^12
=10000*1.051162
=10511.62

Compound interest, compounded monthly

• Math -

Okay where did the 6% came in from?

• Math -

The 6% is an example for the definition of the symbol R. Sorry if it misled you!

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