# Just about everything Prof Grinnell wrote on the board.

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Published on 31 Oct 2010

Department

Mathematics

Course

MATA32H3

Professor

09/22/10

Mathematics of Finance

§ 5.1 Compound Interest Formula

S = P(1 + r)n = P(1 + a/k)kt

P = principal r = periodic interest rate

n = # of compounding periods S = compound amount

a = APR (annual percentage rate) t = time (# of years)

r = a/k n = k/t

NB: Interest is always paid right @ the very end of each compounding period.

Ex Invest $10k @ 3.05% APR compounding monthly for 5 years.

a) S = compounding amount

= P(1 + a/k)kt

= 10,000(1 + 0.0305/12)(12)(5)

§ 11,645.17

b) Period rate = r = a/k

= 0.0305/12

§ 0.002542

c) Compound Interest = S ² P

§ 1,645.17 (from part a)

d) How long for the amount to reach $15k?

15,000 = 10,000(1 + 0.0305/12)12t

Solve for t 3/2 = (1 + 0.0305/12)12t

ln (1.5) = ln [(1 + 0.0305/12)12t]

1 = 12t ln (1 + 0.0305/12)

ln (1.5)

t = ln (1.5)

12 ln (1 + 0.0305/12)

§ 13.31 years

We take 13 years and 4 months.

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