1. 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

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?

3. 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?

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

5. 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.

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) –uniform series –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. 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

11. 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.

12. P=A(P/A 7,5 )=2000(4.1002) EOYCash Flow 0Answer: P=$8,200.40 1$2,000 2 3 4 5

13. 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.

14. P’=A(P/A 7,5 )=$8,200.40 P=P’(P/F 7,2 ) EOYCash Flow 0Answer: P=$7,162.23 1$0 2P’ occurs at year 2: $0 3$2,000 4 5 6 7

15. Deferred Withdrawal Deferring the withdrawal for two years reduces the amount of deposit by $1,038.17 ($8,200.40-$7,262.23)

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 How much can be withdrawn each year in order to deplete the fund w/ the last withdrawal?

17. Find A given P EOYCash Flow 0-$10,000 1-10$A=? A=P(A/P 7,10 )=10,000(.1424) A=$1,424

18. 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?

19. Find A given P EOYCash Flow 0-$10,000 1$0 2 3 through 12A=? P 2 =P(F/P 7,2 )=$11,449 A=P 2 (A/P 7,10 )=$11,449(.1424)=$1,630.34 A=$1,630.34 Delaying the first withdrawal increases the size of each withdrawal by $206 ($1630-$1424)

20. 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?

21. Find A given F EOYCash Flow 0$0 1-35-$A 35$150,000 A=F(A/F 8,35 )=150,000(.0058) ANSWER: A=$870

22. 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?

23. Find F given A EOYCash Flow 0$0 1-30-$1,000 30$F=? F=A(F/A 8,30 )=1,000(113.283) ANSWER: F=$113,283

24. Next lecture Gradient Series