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Chapter 10 Section 1

Chapter 10 Section 1. Interest. Terms. Interest : Fee that is paid for the use of money Principal : Amount of initial deposit or initial/current balance Compound Amount : Amount to which the principal grows (after the addition on interest). Alternate term: Balance Compounded : Computed.

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Chapter 10 Section 1

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  1. Chapter 10 Section 1 Interest

  2. Terms • Interest : Fee that is paid for the use of money • Principal : Amount of initial deposit or initial/current balance • Compound Amount : Amount to which the principal grows (after the addition on interest). Alternate term: Balance • Compounded : Computed

  3. Compound Periods • The number of times interest is compounded in a single year • Denoted by : m • Table 2 (page 470)

  4. Compound Periods Table

  5. Annual Interest Rate • Denoted by : r • Also known as Nominal Rate or Stated Rate. • Number which is stated / advertised and used to calculate the interest rate per period. • Use decimal form when calculating by hand.

  6. Interest Rate Per Compound Period • Denoted by : i • Number which is used to calculate interest for each compounding period. • Use decimal form when calculating. • Formula on next slide (page 470 – Blue-gray box).

  7. Interest Rate Per Period Formula • Formula: i = r / m where r = annual interest rate ( in decimal form) m = number of compound periods in a year

  8. Example of Interest Rate Per Period • Find the interest rate per period of an account that earns 6.25% interest compounded weekly. • Solution: Given: r = 0.0625 and m = 52 i = r / m = 0.0625 / 52 ~ 0.00120 Interest rate per period is approximately 0.12 %

  9. Compound Interest Problems • Basic idea for compound interest accounts • Deposit an initial amount of money into an account. • Step back and watch it grow. • You do not deposit or withdraw any additional money while interest is accumulating.

  10. Diagram for Compound Interest Balances: B0 B1 B2 B3 B4 Interest: i ·B0 i ·B1 i ·B2 i ·B3 … Deposits or Withdraws P B = Balance P = Principal = Initial Deposit Each tick mark represents a compound period

  11. Balance for Compound Interest New balance based on the old balance Bnew = Bprevious + i·Bprevious which simplifies to Bnew = (1+ i)Bprevious (Note that this is in the form of a difference equation) Note that i·Bprevious represents the amount of interest that one earns for the compound period

  12. Balance after n interest/compounding periods F = ( 1 + i )n·P Where: F = compounded amount after n compounding periods. P = Principal (in the form of an initial deposit or current balance).

  13. Notational Differences

  14. Accessing the TVM Solver • Hit APPS key • Select 1:Finance function (Hit ENTER key) • Select 1:TVM Solver …function (Hit ENTER key)

  15. TVM Solver Variables • N = Number of compound periods • I% = Annual Interest Rate (in percent form ( r% )) • PV = Principal Value (or) “Previous/Current” Balance • PMT = Rent / Payment Per Compound Period • FV = Future Value • P/Y = Payments Per Year = m • C/Y = Compounding Periods Per Year = m • PMT:END = Payments(/Interest) made(/calculated) at the end of the compounding period

  16. Using the TVM Solver • Enter the numbers for each variable of interest. • Move the cursor to the variable that you want to solve for. • Hit the ALPHA (green) key and then the ENTER (/solve) key. • The answer will appear next to the variable that you are solving for.

  17. When using the TVM Solver on the calculator • Think: • Outflow = NEGATIVE cash flow (i.e. You DO NOT have the instantaneous use of your money ) • Inflow = POSITIVE cash flow (i.e. You do have the instantaneous use of your money )

  18. Exercise 5 (page 477) Formula Solution • Calculate the compound amount of $1,000 after 2 years if deposited at 6% interest compounded monthly. • Solution: n = 2 ·12 = 24 i = r/m = 0.06/12 = 0.005 F = ( 1 + i )n·P F = ( 1 + 0.005 )24·1000 F = ( 1.12715977…)·1000 F = 1127.15977 Answer :$1,127.16

  19. Exercise 5 (page 477) TVM Solver Solution • Calculate the compound amount of $1,000 after 2 years if deposited at 6% interest compounded monthly. • Solution: N = 2 ·12 = 24 I% = 6 PV = – 1000 PMT = 0 FV = 1127.159776 P/Y = C/Y = 12 Set cursor on FV and Solve ( ALPHA key and then ENTER key) Note the negative sign!!! Answer :$1,127.16

  20. Effective Rate of Interest • Page 474 • Used to • Compares two annual interest rates that have two different yearly compounding periods. • When money from the interest is reinvested in the account, will tell you the ‘true’ interest rate that you are earning.

  21. Effective Rate of Interest Formula Formula: reff = ( 1 + i )m – 1 where: reff = Effective Rate of Interest i = Interest Rate Per Period = r / m m = Number of compounding periods in a single year

  22. Effective Rate of Interest on the Calculator • Access • Hit APPS key • Select 1:Finance function • Use down (or up) arrow key to select C: Eff( function • Syntax Eff( r% , m ) ( r% = Annual Interest Rate in % form)

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