ECE 192 - Time Value of Money

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Last updated 12:42 AM on 7/5/26
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17 Terms

1
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Interest =

difference between amount of money repaid later and money lent today

2
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Principle Amount =

P, amount of money today

3
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Future Amount =

F, money repaid later

<p>F, money repaid later</p>
4
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interest rate =

percent per time period

  • default = annual

5
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interest period =

the time period interest is calculated

  • annual, weekly, daily, etc

6
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future worth and present value =

if P → F at the end of the period

  • P = present value of F

  • F = future value of P

<p>if P → F at the end of the period</p><ul><li><p>P = present value of F</p></li><li><p>F = future value of P</p></li></ul><p></p>
7
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Compound Interest Method =

money earned at the end of a period IS reinvested

formula:

  • F = P(1 + i)N

    • N = # of periods

    • i = interest rate

  • Ic = F - P

<p>money earned at the end of a period IS reinvested</p><p></p><p>formula:</p><ul><li><p>F = P(1 + i)<sup>N</sup></p><ul><li><p>N = # of periods</p></li><li><p>i = interest rate</p></li></ul></li><li><p>I<sub>c</sub> = F - P</p></li></ul><p></p>
8
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Simple Interest Method =

money earned at the end of a period IS NOT reinvested

formula:

  • F = P(1 + iN)

    • N = # of periods

    • i = interest rate

  • Is = PiN

9
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simple vs compound interest method =

compound:

  • increases exponentially

simple:

  • increases linearly

<p>compound:</p><ul><li><p>increases exponentially</p></li></ul><p>simple:</p><ul><li><p>increases linearly</p></li></ul><p></p>
10
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nominal interest rate =

annual interest rate from sub-period interest rate * # of periods

formula:

  • ir = is * m

    • ir = nominal interest rate

    • is = interest rate per sub-period m

    • m = # of sub periods in one year

11
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future amount formula w/ nominal interest rate =

F = P(1 + is)mN = P(1 + ir/m)mN

  • ir = nominal interest rate

  • is = interest rate per sub-period m

  • m = # of sub periods

12
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effective interest rate =

the actual interest rate if converted to a one year compounding period

formula

  • ie = (1 + ir/m)m - 1 = (1 + is)m - 1

    • ir = nominal interest rate

    • is = interest rate per sub-period m

    • m = # of sub periods

13
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nominal vs effective interest rate =

if m > 1:

  • effective > nominal

if m = 1:

  • effective = nominal

<p>if m &gt; 1:</p><ul><li><p>effective &gt; nominal </p></li></ul><p>if m = 1:</p><ul><li><p>effective = nominal</p></li></ul><p></p>
14
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continuous compounding effective interest rate =

ie = eir - 1

if sub-periods are infinitesimally small

15
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what interest period grows fastest =

continuous > daily > monthly > …

<p>continuous &gt; daily &gt; monthly &gt; …</p>
16
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cash flow diagrams =

graph to show cash flows magnitude and when it occurs

axis:

  • horizontal = time

  • vertical = size/direction

    • up = positive

    • down = negative

    • numbers = magnitude of cash flow

cash flows can be added or subtracted if they occur at the same period

<p>graph to show cash flows magnitude and when it occurs</p><p></p><p>axis:</p><ul><li><p>horizontal = time</p></li><li><p>vertical = size/direction</p><ul><li><p>up = positive</p></li><li><p>down = negative</p></li><li><p>numbers = magnitude of cash flow</p></li></ul></li></ul><p></p><p>cash flows can be added or subtracted if they occur at the same period</p><p></p>
17
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equivalence =

two cash flows, Ft+N and Pt, are equivalent w/ respect to i if

  • Ft+N = Pt(1 + i)N

  • Ft+N+M = Pt(1+i)N+M = Ft+N(1+i)M

<p>two cash flows, F<sub>t+N </sub>and P<sub>t</sub>, are equivalent w/ respect to i if</p><ul><li><p>F<sub>t+N </sub>= P<sub>t</sub>(1 + i)<sup>N</sup></p></li><li><p>F<sub>t+N+M</sub> = P<sub>t</sub>(1+i)<sup>N+M</sup> = F<sub>t+N</sub>(1+i)<sup>M</sup></p></li></ul><p></p>