FINANCIAL MATHEMATICS Chapter 13 FINANCIAL MATHEMATICS Today’s Topics: ⊲Simple Interest ⊲Compound Interest ⊲Rule 72 ⊲Fixed Term Deposits

Are you interested in interest? Simple Versus Compound

A Review of Simple Interest SIMPLE INTEREST Is: Simple (to compute) Interest paid only on the original principal, C, Also referred to as flat rate interest Use the following simple interest formula: I = C × r × n where C is the principal or money deposited, r is the simple interest per annum as a decimal, n is time expressed in terms of years

A Review of Compound Interest Compound interest is the interest earned not only on the original principal, but also on all interests earned previously. In other words, at the end of each year, the interest earned is added to the original amount and the money is reinvested. A = C x (1 + r/100)n I = C x (1 + r/100)n - C This means that the interest is added to the principal each period so that the principal continues to grow throughout the life of the loan or investment. Remember, to find total interest earned from the beginning of the loan or investment to the end, subtract the principal from the final balance

Compound Interest Formulas A = C x (1 + r/100)n I = C x (1 + r/100)n - C A = Future Value or Final Balance C = Present Value or Principal R = Interest rate per compound period N = the number of periods compounded

Simple Interest Compound Interest Compounding interest is "interest on interest." It is a method of calculating interest where the interest is added to the original principal. This new value is now our principal for the next time period. In this method the interest earned in past terms can earn interest in future terms. Simple interest is a type of interest that is paid only on the original amount deposited and not on past interest paid.

(NOTE: preferably use y8 – y0) Let’s Use the Equation Solver Feature of the Graphing Calculator to Compute Simple Interest Prepare to write the keystrokes for computing simple interest into your notes. Solve the Interest Formula: I = C x R x N for zero like so: Zero = (C x R x N) – I Place this expression in the equation editor. (NOTE: preferably use y8 – y0) Keystrokes Cont’d: Math, ↑ENT (or 0) , VARS, YVARS, ENT, FC# You will see the variable prompts. Fill in all variables provided in the problem and solve for the one missing by going to the entry and pressing “Alpha, Solve”/ “Alpha, ENT”

Use the Equation Solver Feature of the GDC to Compute Periodic Repayments Too! Write the keystrokes for calculating periodic repayments in your notes Solve the Repayment Formula: Rp = (C + I)/N for zero i.e. Repayment = (Principal + Interest)/# of Repayments Zero = (C + I)/N – Rp Place this expression in the equation editor. (NOTE: preferably use y8 – y0) Remaining Keystrokes: Math, ↑ENT (or 0), VARS, YVARS, ENT, FC# You will see the variable prompts. Fill in all variables provided in the problem and solve for the one missing by going to the entry and pressing “Alpha, Solve”/ “Alpha, ENT”

Let’s Practice Solving Simple Interest Problems using the equation Solver: Turn in your books to page 427. Work Ex 9 to practice the keystrokes you just learned. Also, Work Ex 13 on pages 429-430. Meanwhile, I will prepare ELMO for your viewing so that we can verify calculator keystrokes and practice problems together.

the graphing calculator can also solve compound interest First, since this unit is dealing with financial math, set your decimal to float 2 places Keystrokes: Mode, float, 2 Next, choose APPS, 1 – Finance, 1 – TVM Solver Your screen should look like this!!!

Financial Math: TVM Solver PV = 0.00 PMT = 0.00 FV = 0.00 P/Y = 1.00 C/Y = 1.00 PMT: END BEGIN See Investigation 1 for meanings: p434 N (number of payments/time periods) I% (interest rate) PV (present value of the investment) FV (future value of the investment) P/Y (number of payments per year) C/Y (number of compounding periods per year)

TVM Solver - Time Value of Money Manager(TVM) FYI TVM Solver - Time Value of Money Manager(TVM) Use time-value-of-money (TVM) functions (menu items 2 through 6) to analyze financial instruments such as annuities, loans, mortgages, leases, and savings Each TVM function takes zero to six arguments, which must be real numbers. The values that you specify as arguments for TVM functions are not stored to the TVM variables Note: To store a value to a TVM variable, use the TVM Solver or use STO and any TVM variable on the FINANCE VARS menu.

FINANCIAL CALCULATIONS To display the FINANCE CALC menu, press APPS, ENT. CALC VARS 1: TVM Solver... : Displays the TVM Solver. 2: tvm_Pmt : Computes the amount of each payment. 3: tvm_I%: Computes the interest rate per year. 4: tvm_PV: Computes the present value. 5: tvm_N: Computes the number of payment periods. 6: tvm_FV: Computes the future value. 7: npv(: Computes the net present value.

The Previous slide shows the meanings of the abbreviations used in Financial Calculations and Financial Math. To use that feature, we must place all given variables in parenthesis. The missing variable is automatically solved for if this method is used. We will practice using the TVM Solver Only!!! For an example on how to compute compound interest variables using the TVM solver, see the next slide.

Let’s Practice Using the TMV Solver Go to page 431 of your textbook. It reads: Calculate the interest paid on a deposit of $6000 at 8% p.a. (per annum) compounded annually for 3 years. Keystrokes: Float: 2, APPS, ENT, ENT N= 36 payments (3 years) I%= 8.00 PV = -6000.00 PMT=0.00 FV = ? P/Y = 12 (1 year) C/Y = 12 (1 year)

Follow along with the video for extra practice using the TVM Solver Here’s a You Tube Video!!! Watch This - Follow along with the video for extra practice using the TVM Solver Click on the Link Below http://www.youtube.com/watch?v=Ku4VPMSP2xM&feature=related

Other Concepts To Know… Fixed Term Deposits Effective/Effective Rate These deposits are ‘locked away’ by a financial institution for a fixed time period of one month to ten years at a FIXED rate. Interest is accrued or compounded, therefore the principal or deposit increases during the fixed term. The longer the money is locked away the better! Typical Question: Find the effective after tax return if the investor’s tax rate is 48.5 cents in the dollar (i.e. 48.5%) Turned to p.441 The effective rate is the interest rate compounded annually. R = (1 + i)c - 1

Let’s Try to Watch this You Tube Video - Last Concept – Rule of 72 The rule of 72 is used to figure out when your money will double. If you divide 72 by the interest rate you are earning (or paying) the answer will give you the number of years until your money doubles. This rule only works on interest that is compounded once a year. See IVG 1 – How Long Will It Take To Double My $? Let’s Try to Watch this You Tube Video - http://www.youtube.com/watch?v=Ldvvgvst75w

THE END THAT’s IT!!! Is the USD weak or strong? ASSIGNMENT: Group Work - (See Syllabus) TOPIC FOR NEXT CLASS: Foreign Exchange QUESTION TO PONDER: Is the USD weak or strong?   THE END