CTC 475 Review

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CTC 475 Review

• Simple vs Compound Interest
• Find F given P
• (equation and factor form)
• Find P given F
• (equation and factor form)
• Find i given P, F and n
• Find n given P, F and i

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Single Sum-Practice

• A one-time deposit of 2,000 is made into an
  account that earns 4 yearly. What is the
  account worth after 40 years?

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Single Sum-Practice

• In 1979 gasoline was 0.25 a gallon. In 2009
  gasoline was 2.00 a gallon.
• What was the average yearly inflation rate?

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Single Sum-Practice

• How long does it take to double money if an
  account earns 5 yearly?

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Single Sum-Practice

• What one-time deposit should be made into an
  account so that the money grows to 15,000 18
  years later? Assume the account earns 5 yearly.

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CTC 475

• Uniform Series

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Objectives

• Know what a uniform series is
• Know how to
• Find F given A
• Find P given A
• Find A given F
• Find A given P

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Uniform Series

• All cash flows in a series are the same amount
  (A)
• uniform series
• annual series
• annuity

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Uniform Series (4 cases)

• Find P given A
• Present worth factor
• Find A given P
• Capital recovery factor
• Find F given A
• Future worth factor
• Find A given F
• Sinking fund factor

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Rules for Uniform Series

• P occurs one period before the first cash flow A
• F occurs at the same time as the last A
• (last A or deposit earns no interest)
• nnumber of A cash flows

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Find P given A

• How much must be deposited in a fund today in
  order to w/draw 2,000 per year for 5 years? The
  fund pays 7 per year compounded annually. The
  first withdrawal occurs 1 year after the deposit.

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PA(P/A7,5)2000(4.1002)
EOY Cash Flow
0 Answer P8,200.40
1 2,000
2 2,000
3 2,000
4 2,000
5 2,000
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Deferred Withdrawal

• How much must be deposited in a fund today in
  order to w/draw 2,000 per year for 5 years? The
  fund pays 7 per year compounded annually. The
  first withdrawal occurs 3 years after the deposit.

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PA(P/A7,5)8,200.40PP(P/F7,2)
EOY Cash Flow
0 Answer P7,162.23
1 0
2 P occurs at year 2 0
3 2,000
4 2,000
5 2,000
6 2,000
7 2,000
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Deferred Withdrawal

• Deferring the withdrawal for two years reduces
  the amount of deposit by 1,038.17
  (8,200.40-7,262.23)

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Find A given P

• 10,000 is deposited in a fund paying 7
  compounded annually. 10 equal annual withdrawals
  are made, with the first withdrawal occurring one
  year after the deposit. How much can be
  withdrawn each year in order to deplete the fund
  w/ the last withdrawal?

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Find A given P
EOY Cash Flow
0 -10,000
1-10 A?
AP(A/P7,10)10,000(.1424) A1,424 AP(A/P7,10)10,000(.1424) A1,424
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Deferred withdrawal

• 10,000 is deposited in a fund paying 7
  compounded annually. 10 equal annual withdrawals
  are made, with the first withdrawal occurring
  three years after the deposit. How much can be
  withdrawn each year in order to deplete the fund
  w/ the last withdrawal at year 12?

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Find A given P
EOY Cash Flow
0 -10,000
1 0
2 0
3 through 12 A?
P2P(F/P7,2)11,449 AP2(A/P7,10)11,449(.1424)1,630.34 A1,630.34 Delaying the first withdrawal increases the size of each withdrawal by 206 (1630-1424) P2P(F/P7,2)11,449 AP2(A/P7,10)11,449(.1424)1,630.34 A1,630.34 Delaying the first withdrawal increases the size of each withdrawal by 206 (1630-1424)
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Find A given F

• If 150,000 is to be accumulated in 35 years, how
  much must be deposited each year in a fund which
  pays 8 compounded annually?

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Find A given F
EOY Cash Flow
0 0
1-35 -A
35 150,000
AF(A/F8,35)150,000(.0058) ANSWER A870 AF(A/F8,35)150,000(.0058) ANSWER A870
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Find F given A

• Annual deposits of 1,000 are made into a savings
  account for 30 years the account pays interest
  at a rate of 8 compounded annually. How much
  will be in the account immediately after the last
  deposit?

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Find F given A
EOY Cash Flow
0 0
1-30 -1,000
30 F?
FA(F/A8,30)1,000(113.283) ANSWER F113,283 FA(F/A8,30)1,000(113.283) ANSWER F113,283
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Next lecture

• Gradient Series