# Just about everything Prof Grinnell wrote on the board.

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School
UTSC
Department
Mathematics
Course
MATA32H3 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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