Theory of Interest (TOI 152) Notes FULL SEMESTER

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THEORY OF INTEREST 152:

K Capital amt / Present value PV
S Accumulated amt / Future value FV
i Effective interest rate per year I/YR
- 1nce per year
(m)
i Nominal interest rate per year I/YR
- more than 1nce per year
m No. of times per year interest is earned P/YR
n How many years P/YR
N How many interest periods (m x n) P/YR
Chapter 1 → Simple and Compound Interest

Simple Interest:
- interest earned in n years = FV – PV = PV(ni)

FV = PV(1 + ni)

Compound Interest:
- interest earned in n years = FV – PV
- interest earned in the “rth” year = FVr – FVr-1

FV = PV(1 + i)n

Nominal Compound Interest:
- when there are m interest periods per year (m > 1)
- thus mn periods for the n years

FV = PV(1 + i(m)/m)mn




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The Discounting Factor:
- Vin is the discounting factor
o used to denote (1 / (1+i))n
- PV of a FV is called the discounted value of the FV

Nominal and Effective Interest Rates:
- im p.u.p.a = nominal annual
- i p.u.p.a = effective annual
- im / m p.u.p.p = effective periodic

- if two of the above earn the same amount of interest for one
year (n = 1)
o they are corresponding or equivalent rates
(1+i) = (1 + (im / m))m

- if more or less than one year (n ≠ 1)
o they are corresponding if:
(1 + (in / n)) = (1 + (im / m))m

Continuous Compounding (Force of Interest):
- interest is compounded continuously
- K units of capital invested at a force of interest (r p.u.p.a.) for n
years (e = 2.7182818).
FV = PVenr

- annual effective interest rate (i) that will correspond to the
annual force of interest where:
o 1 + i = er
o corresponding r is r = loge (1 + i) = 1n(1 + i)




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