Department

MathematicsCourse Code

MATA32H3Professor

Karimian Pour, C.Study Guide

MidtermThis

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Compound Interest Formula

S=P(1+r)^n

r = compound interest rate or periodic interest rate (amount of interest paid after a fixed

compound)

n = number of interest payments 1 2 3 4

S = compound amount

P = principle (amount invested) start end

Time

S=P(1+a/k)^kt

a = annual rate

k = compounded frequency/year

t = time or number of years

Example:

$10,000 invested. 3.05% annual rate compounded monthly for 5 years.

P= $10,000

a= 3.05% S=P(1+a/k)^kt

k= 12 S=10,000 (1+0.0305/12)^60

t= 5 = 11,645.17

S=11,645.17

*to ONLY find interest amount, take S-P

S-P

11,645.17-10,000

=1,645.17

Interest amount is 1,645.17

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Effective Rate of Interest

Suppose you invest P at r% APR compounding n times annually.

1 year

P S

P(1+r/n)^n

re is the effective rate of interest. re=(1+r/n)^n-1

The special rate of simple interest that yields the same amount as compounded interest.

*simple interest – interest paid once a year (at the end of the year)

effective interest is also paid at the end of the year

re is bigger than r [binomial theorem]

when n is 1, ER and APR are the same

P(1+re) = P(1+r/n)^n

Example:

a=5% k=365 daily interest = 0.05/365

(1+0.05/365)^365 -1

= 0.0512657

= 5.12657%

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Equation of Value

2 types: payments and debts

At all times, value of payment = value of debt

Example:

$32,000 owed at 6 years $10,000 paid

3.6 APR compounded quarterly

Find the balance payment

0 1 2 3 4 5 6

$10,000 $32,000

At t=6, the value of debt is $32,000 and the value of payment is x.

t=6 k=24 a=0.036

$20,035.86 owed

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