1. CTC 475 Review Simple vs Compound Interest Find F given P
(equation and factor form)
Find P given F
Find i given P, F and n
Find n given P, F and i

2. 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?
Answer: $9,602

3. Single Sum-Practice
In 1979 gasoline was $0.25 a gallon. In 2018 gasoline was $2.65 a gallon.
What was the average yearly inflation rate?
Answer: 6.24%

4. Single Sum-Practice
How long does it take to double money if an account earns 5% yearly?
Answer: 15 years

5. Single Sum-Practice
What one-time deposit should be made into an account so that the money grows to $15, years later? Assume the account earns 5% yearly.
Answer: $6,233

6. CTC 475
Uniform Series

7. 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

8. Uniform Series All cash flows in a series are the same amount (A)
annual series
annuity

9. 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

10. Uniform Series Easiest to use factor tables in the back of your book
Equations are located in the front of your book (open book cover)

11. 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)
n=number of A cash flows

12. 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.

13. P=A(P/A7,5)=2000(4.1002) EOY Cash Flow Answer: P=$8,200.40 1 $2,000 2
Answer: P=$8,200.40 1
$2,000 2 3 4 5

14. Find P given A 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.

15. P’=A(P/A7,5)=$8,200.40 P=P’(P/F7,2)
EOY
Cash Flow
Answer: P=$7,162.23 1 $0 2
P’ occurs at year 2: $0 3
$2,000 4 5 6 7

16. Deferred Withdrawal
Deferring the withdrawal for two years reduces the amount of deposit by $1, ($8, $7,262.23)

17. 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 How much can be withdrawn each year in order to deplete the fund w/ the last withdrawal?

18. Find A given P EOY Cash Flow -$10,000 1-10 $A=?
-$10,000
1-10
$A=?
A=P(A/P7,10)=10,000(.1424)
A=$1,424

19. Find A given P 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?

20. Find A given P EOY Cash Flow -$10,000 1 $0 2 3 through 12 A=?
-$10,000 1 $0 2
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)

21. 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?

22. Find A given F EOY Cash Flow $0 1-35 -$A 35 $150,000$0
1-35
-$A 35
$150,000
A=F(A/F8,35)=150,000(.0058)
ANSWER: A=$870

23. 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?

24. Find F given A EOY Cash Flow $0 1-30 -$1,000 30 $F=?$0
1-30
-$1,000 30
$F=?
F=A(F/A8,30)=1,000( )
ANSWER: F=$113,283

25. Next lecture
Gradient Series