CTC 475 Review 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

Single Sum-PracticeSingle 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?

Single Sum-PracticeSingle 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?

Single Sum-PracticeSingle Sum-Practice• How long does it take to double

money if an account earns 5% yearly?

Single Sum-PracticeSingle 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.

CTC 475 CTC 475 Uniform SeriesUniform Series

ObjectivesObjectives• 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

Uniform Series Uniform Series

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

Uniform Series (4 cases)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

Rules for Uniform SeriesRules 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)

• n=number of A cash flows

Find P given AFind 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.

P=A(P/AP=A(P/A7,57,5)=2000(4.1002))=2000(4.1002)EOY Cash Flow

0 Answer: P=$8,200.40

1 $2,000

2 $2,000

3 $2,000

4 $2,000

5 $2,000

Deferred WithdrawalDeferred 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.

P’=A(P/AP’=A(P/A7,57,5)=$8,200.40)=$8,200.40P=P’(P/FP=P’(P/F7,27,2))

EOY Cash Flow

0 Answer: P=$7,162.23

1 $0

2 P’ occurs at year 2: $0

3 $2,000

4 $2,000

5 $2,000

6 $2,000

7 $2,000

Deferred WithdrawalDeferred Withdrawal• Deferring the withdrawal for two

years reduces the amount of deposit by $1,038.17 ($8,200.40-$7,262.23)

Find A given PFind 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?

Find A given PFind A given PEOY Cash Flow

0 -$10,000

1-10 $A=?

A=P(A/P7,10)=10,000(.1424)

A=$1,424

Deferred withdrawalDeferred 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?

Find A given PFind A given PEOY Cash Flow

0 -$10,000

1 $0

2 $0

3 through 12 A=?

P2=P(F/P7,2)=$11,449

A=P2(A/P7,10)=$11,449(.1424)=$1,630.34

A=$1,630.34

Delaying the first withdrawal increases the size of each withdrawal by $206 ($1630-$1424)

Find A given FFind 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?

Find A given FFind A given FEOY Cash Flow

0 $0

1-35 -$A

35 $150,000

A=F(A/F8,35)=150,000(.0058)

ANSWER: A=$870

Find F given AFind 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?

Find F given AFind F given AEOY Cash Flow

0 $0

1-30 -$1,000

30 $F=?

F=A(F/A8,30)=1,000(113.283)

ANSWER: F=$113,283

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