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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-Practice.

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CTC 475 Review

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  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/A7,5)=2000(4.1002)

  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/A7,5)=$8,200.40P=P’(P/F7,2)

  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

  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

  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

  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

  24. Next lecture • Gradient Series

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