Texas Instruments 83 Plus and 84 Plus Calculator

Transcription

1 Texas Instruments 83 Plus and 84 Plus Calculator For the topics we cover, keystrokes for the TI-83 PLUS and 84 PLUS are identical. Keystrokes are shown for a few topics in which keystrokes are unique. Start by reading the Quik Start section. Then, before beginning a specific unit of the text, check to see if this includes keystrokes for that unit. Going through the keystrokes before class will help, especially if your instructor cannot include instructions for your calculator during class. Quik Start Calculator registers. Some keys have 2 functions and some have 3. One appears in white on the face of the key. Some appear in blue above the key, on the left. Others appear in green above the key, on the right. To access the function appearing in blue, press [2ND] first. To access the function appearing in green, press [ALPHA] first. Menus. The TI-83 Plus and 84 Plus have menus. Once in a menu, several choices will appear in the display. To move the cursor up, down, left, or right use the 4 scroll keys located at the upper right part of the calculator. Once the cursor is in the right spot, press [ENTER]. To return to the main screen, press [2ND] [QUIT]. Display. To darken the display contrast, press [2ND], then hold down the [ > ] scroll key. To lighten the display, press [2ND], then hold down the [? ] scroll key. The display shows several lines; for simplicity, only part of the characters may be shown in keystroke solutions. Arithmetic. Arithmetic can be done as shown below. Example: Multiply,222 by 32.8,222 [ ] 32.8 [ENTER] 40,08.60 answer Notice, when keying in,222 we did not key in a comma (there is no comma key). The comma is shown in keystrokes for clarity. Also, notice that we did not key in the decimal point when entering,222; the calculator presumes there is a decimal point at the far right. Correcting entries. To erase the last digit entered, press [ = ], then [DEL]. Pressing [CLEAR] during an operation clears that operation. Pressing [CLEAR] after an operation is finished clears the display. Negative numbers. To enter a negative number, press the ( ) sign on the bottom row of keys. Notice, this is different than the minus key located above the + symbol. Setting the decimal. To change the number of displayed decimal places, first press [MODE]. Then, move the cursor to either Float (for a floating decimal), or over the number of digits (such as 2 or 5), located to the right of Float. Then press [ENTER], followed by [2ND] [QUIT]. Time-saving registers. Suppose we want to calculate the total monthly rent on a 72-unit apartment building in which 36 units rent for $850 each, 24 rent for $900 each, and 2 rent for $925 each. One approach would be to write down subtotals, then add subtotals: Here s another approach: 36 $850 $30, $900 2,600 2 $925 +,00 Total $63, [ ] 850 [ENTER] 30, first subtotal [ + ] 24 [ ] 900 [ENTER] 52, second subtotal added to first [ + ] 2 [ ] 925 [ENTER] 63, third subtotal added to previous running total

2 Unit 3. Mathematical symbols and expressions 2 5 Example 2 Use a calculator to find the value of: a. 23 b [ x ] [ENTER] result 4 [ v ] 5 [ENTER] result Chapters 0 & Compound interest formulas Using a calculator properly is essential in working with the compound interest formulas of Illustration 0-. An example will be given for each of the 8 compound interest formulas. We will begin with Formula A. Before starting, here are a few things worth noting: C There are several ways to do the arithmetic; the keystrokes shown in this section are only one choice. The keystrokes shown may, in some cases, be longer than another method but are used because the method is considered to be more conceptually sound and easier to remember. C Here is a tip: Try your own keystrokes before looking at ours. If your approach makes sense, use it because it will be easier to remember. If you have difficulty, then review our suggested keystrokes. C The displayed values shown in the keystrokes have 2 decimal places. Having our decimal set at more or less places will not affect the final answer, provided we use chain calculations (remember that chain calculations use the internal, more accurate value, not the displayed value). Formula A Example of Unit 0.2 You get an income tax refund of $,700 and deposit the money in a savings plan for 6 years, earning 6% compounded quarterly. Find the ending balance using compound interest formulas. n 24 FV = PV ( + i) = $,700 (.05) = $2, [ v ] 24 [ENTER] to the 24th power [ ],700 [ENTER] 2,430.5 answer Example 2 of Unit 0.2 Suppose a wise man had deposited $ in a savings account 2,000 years ago and the account earned interest at 2% compounded annually. If the money in the account today were evenly divided among the world s population, how much would each person receive, based on a world population of 7 billion? n 2000 FV = PV ( + i) = $ (.02) Then divide by 7,000,000, [ v ] 2,000 [ENTER].59E7 account balance, in scientific notation [ ] 7,000,000,000 [ENTER] 22,659, amount per person

3 Formula B Example 4, Unit 0.2 You deposit $00 at the end of each year for 4 years, earning 6% compounded annually. Use compound interest formulas to find the balance in 4 years. FV ' PMT ( % i)n & i $00 (.06)4 & = = $ [ v ] 4 [ENTER].26 th.06 to the 4 power [ - ] [ENTER].26 value of numerator [ ].06 [ENTER] 4.37 value inside of brackets [ ] 00 [ENTER] answer Formula 2A Example of Unit 0.3 Your aunt says she will give you $2,430.5 in 6 years. Assuming that you can earn 6% compounded quarterly, what is the real value of her promise, in today s dollars? PV ' FV ( % i) ' $2,430.5 n (.05) 24 = $, ,430.5 [ ] 2,430.5/ ready to divide (.05 [ v ] 24 ) [ENTER], answer Formula 2B Example 2 of Unit 0.3 You are selling a valuable coin. You have two offers. The first offer is for $5,500 cash. With the second offer, the buyer will pay you $2,000 at the end of each year for 3 years. Assuming that you can earn 8% compounded annually on your money, which offer is better? PV ' PMT & ( % i) n i & (.08) = $2,000 3 = $5, [ ].08 [ v ] 3 [ENTER].79 over (.08 to the third power) [ ] [ ( ) ] [ENTER] -.79 changed the sign [ + ] [ENTER].2 value of the numerator [ ].08 [ENTER] 2.58 value inside the brackets [ ] 2,000 [ENTER] 5,54.9 answer

4 Formula 3 Example of Unit.4 Dale bought a rare baseball card 3 years ago for $,500. He just sold the card for $2,000 to get some money for his college tuition. What interest rate, compounded annually, did Dale earn on the investment? i ' FV PV n & $2,000 = 3 & = % (with 4 decimal places) $,500 2,000 [ ],500 [ENTER].33 value inside of parentheses [ v ] ( [ ] 3 ) [ENTER].0 previous value to the /3 power [ - ] [ENTER].0 rate, in decimal form, with decimal at 2 [ ] 00 [ENTER] 0.06 rate, as a percent, with 2 decimal places Formula 4A Example 2 of Unit. You want to accumulate $200,000 for retirement in 40 years. You can earn 6.75% compounded monthly. What amount must you deposit at the end of each month in order to accumulate $200,000 in 40 years? PMT ' FV (i) ( % i) n & = $200,000 ( ) = $8.7 ( ) 480 & [ v ] 480 [ENTER] 4.77 th to the 480 power [ - ] [ENTER] 3.77 value of denominator [STO] [ALPHA] [ A ] [ENTER] 3.77 stored the value in register A 200,000 [ ] [ENTER],25.00 value of numerator [ ] [ALPHA] [ A ] [ENTER] 8.7 answer Formula 4B Example 2 of Unit.2 Suppose you have accumulated $500,000, perhaps from many years of savings or from an inheritance. You put the money in a savings plan earning 6% compounded monthly. You want the plan to last 40 years. How much can you withdraw at the end of each month? PMT ' PV (i) & ( % i) n $500,000 (.005) = = $2,75.07 & (.005) 480 [ ].005 [ v ] 480 [ENTER].09 th over (.005 to the 480 power) [ ] [ ( ) ] [ENTER] -.09 changed the sign [ + ] [ENTER].9 value of denominator [STO] [ALPHA] [ A ] [ENTER].9 stored the value in register A 500,000 [ ].005 [ENTER] 2, value of numerator [ ] [ALPHA] [ A ] [ENTER] 2,75.07 answer

5 Formula 5 Example 3 of Unit. You want to start a restaurant business and estimate it will take $28,000 to get started. You currently have $3,000 and can deposit an additional $425 at the end of each month. If your savings will earn 9% compounded monthly, in how many months can you start your business? For Formula 5 we must use proper sign convention for PV, FV, and PMT: PV = negative $3,000 (negative because you pay this amount into a savings plan) FV = $28,000 (positive because you will get this amount back from the savings plan) PMT = negative $425 (negative because you pay this amount into a savings plan) n ' &ln PV % ( PMT ) i PMT & FV i ln(%i) &ln &$3,000 % &$ &$ & $28,000 = = months ln(.0075) Step : Compute and store (-$425 over.0075) [ ( ) ] 425 [ ].0075 [ENTER] -56, value of ( - $425 over.0075) [STO] [ALPHA] [ A ] [ENTER] -56, stored in register A Step 2: Compute and store the value of the denominator inside of large brackets [ - ] 28,000 [ENTER] -84, value of the denominator inside of large brackets [STO] [ALPHA] [ B ] [ENTER] -84, stored in register B Step 3: Compute and store the value of the main denominator [LN].0075 [ENTER].0 the natural log of.0075 [STO] [ALPHA] [ C ] [ENTER].0 stored in register C Step 4: Compute the value of total numerator [ALPHA] [ A ] [ENTER] -56, recalled the value of ( - $425 over.0075) [ - ] 3,000 [ENTER] -59, value of numerator inside of large brackets [ ] [ALPHA] [ B ] [ENTER].70 total value inside of large brackets [LN] [2ND] [ANS] [ENTER] -.35 the natural log [ ] [( )] [ENTER].35 value of the total numerator Step 5: Find answer [ ] [ALPHA] [ C ] [ENTER] answer

6 Chapters 4, 5, and 9 Financial calculators Keystrokes will be shown for problems in which keystrokes are unique those same examples of the text that show keystrokes for the HP 0BII and the TI BAII PLUS. The TVM registers are accessed through the APPS key. Once in the TVM menu, we scroll to the item we want to enter, key in the value, and press [ENTER]. Once all variables are displayed correctly, we put the cursor on the variable we are solving for, and press [ALPHA] [SOLVE], located above the ENTER key. Remember, TVM problems throughout the text assume the period per year (P/YR) setting is. Keystrokes assume calculator starts out in End mode. Example of Unit 4.2 Sebastian Xavier is a soda pop addict and wonders how much money he could accumulate if he stopped drinking soda pop and deposited the $50 per month he spends on the stuff into a savings plan. Sebastian just turned 20. If his savings plan earns 6% compounded monthly and his first deposit is a month from now, what amount would he have at retirement, 40 years from now? select P/Y then: [ENTER] P/Y=.00 set P/Y to ; leave it there for life select N then: 40 [ ] 2 [ENTER] N= monthly deposits 6 [ ] 2 [ENTER] I%=.50 periodic rate 0 [ENTER] PV=0.00 there is no present value [( )] 50 [ENTER] PMT= monthly deposit Select FV: [ALPHA] [SOLVE] FV= 298,723.6 ending balance Example 2 of Unit 4.2 You have the chance to buy a promissory note in which you would receive 28 quarterly payments of $500, starting 3 months from now. If you want to earn 8% compounded quarterly, what price should you pay for the note? 28 [ENTER] N= quarterly payments 8 [ ] 4 [ENTER] I%=2.00 periodic rate select PMT then: 500 [ENTER] PMT= quarterly payment 0 [ENTER] FV= 0.00 there is no future value select PV: [ALPHA] [SOLVE] PV= -0, price you can pay to earn 8% compounded quarterly Example 5 of Unit 4.3 You deposit $00 at the beginning of each year for 4 years, earning 6% compounded annually. Find the balance in 4 years. 4 [ENTER] N= periods 6 [ENTER] I%=6.00 periodic rate 0 [ENTER] PV=0.00 there is no one-time initial deposit [( )] 00 [ENTER] PMT= annual deposit select BEGIN [ENTER] BEGIN now in begin mode select FV: [ALPHA] [SOLVE] FV= answer select END [ENTER] put back in end mode

7 Example of Unit 9. Tara got a $60,000 5-year mortgage loan at 7.25% on April. Calculate her monthly payment. Then, using the amortization registers of your calculator, find interest, principal, and remaining balance for the first two payments. Note: When amortizing with the TI-83 Plus and TI-84 Plus, we can find the interest and/or principal for any series of payments, or the balance after any payment. To find the interest and/or principal, we provide the beginning and ending payment number of that series. To find the balance we provide only the ending payment number. calculate monthly payment 5 [ ] 2 [ENTER] N= months 7.25 [ ] 2 [ENTER] I%=.60 periodic rate 60,000 [ENTER] PV=60, loan amount Select FV: 0 [ENTER] FV=0.00 no future value in this problem Select PMT: [ALPHA] [SOLVE] PMT= -, monthly payment amortize [2nd] [QUIT] must exit TVM menu before amortizing Scroll down to A: [ENTER] ΣInt( asking for payment sequence, [ENTER] interest for payment Scroll down to 0: [ENTER] ΣPrn( asking for payment sequence, [ENTER] principal for payment Scroll down to 9: [ENTER] bal( asking for payment number [ENTER] 59,506.0 balance after payment (see note*) * Note: The ending balance is incorrect ($60,000 original balance - $493.9 principal = $59,506.09, not $59,506.0). Repeat for payment 2 Note: Don t clear calculator; next example is a continuation Example 2 of Unit 9. Refer to Example (above). Calculate interest, principal, and remaining balance for each of the first 3 calendar years. Note: Tara got her loan on April, so she makes 8 payments the first calendar year. keystrokes (continued from Example ) display explanation Select A: [ENTER] ΣInt( asking for payment sequence, 8 [ENTER] -7, interest for first 8 payments Select 0: [ENTER] ΣPrn( asking for payment sequence, 8 [ENTER] -4, principal for first 8 payments Select 9: [ENTER] bal( asking for payment sequence 8 [ENTER] 55,964.2 balance after payment 8 Repeat for second and third calendar years (9-20, 2-32)

8 Example 3 of Unit 9. Refer to Examples and 2 (above). Calculate the total interest Tara will pay on her 5-year loan. keystrokes (continued from Example 2) display explanation Scroll down to A: [ENTER] ΣInt( asking for payment sequence, 80 [ENTER] -02, interest for all 80 payments Scroll down to 0: [ENTER] ΣPrn( asking for payment sequence, 80 [ENTER] -59, principal for 80 payments of $, Scroll down to 9: [ENTER] bal( asking for payment number 80 [ENTER].33 balance after making 80 payments of $, Note: Because of rounding each payment to the nearest penny and because interest for each payment is rounded to the nearest penny, the total principal paid is $59, (33 short), and the balance is $0.33. Tara s final payment must be 33 greater ($,460.9) so the loan will be fully repaid. Tara will make 79 monthly payments of $, and a final payment of $, Example 6 of Unit 9.2 (Condensed). Tara got a $60,000 mortgage loan at 7.25%. Her total loan costs, for APR purposes, is $8,060. Assume Tara will pay off the loan at the end of 7 years. Calculate her real APR, reflecting the early payoff. calculate monthly payment 5 [ ] 2 [ENTER] N= months 7.25 [ ] 2 [ENTER] I%=.60 periodic rate 60,000 [ENTER] PV=60, loan amount Select FV: 0 [ENTER] FV=0.00 no future value to calculate monthly payment Select PMT: [ALPHA] [SOLVE] PMT= -, monthly payment calculate balance after payment 84 (must have decimal at 2) [2ND] [QUIT] must exit TVM menu to amortize [APPS] [ENTER] :TVM ready to select amortization function Scroll down to 9: [ENTER] bal( asking for payment number 84 [ENTER] 06,58.8 balance after payment 84 calculate APR (loan paid off in 7 years) [STO] [ALPHA] [ A ] [ENTER] 06,58.8 stored in register A [APPS] [ENTER] [ENTER] N=80 back in TVM menu To FV: [(& )] [ALPHA] [ A ] [ENTER] FV=-06,58.8 must pay unpaid balance ($06,58.8) in 7 years To PV: 60,000 [ - ] 8,060 [ENTER] PV=5, net proceeds To N: 84 [ENTER] N=84.00 payoff in 84 months Scroll to I%: [ALPHA] [SOLVE] I%=.70 periodic rate, rounded to 2 places [MODE] Select FLOAT, then 9 [ENTER] set decimal at 9 places [2ND] [QUIT] decimal now set at 9 places [APPS] [ENTER] [ENTER] I%= back in TVM menu; periodic rate with more digits write down periodic rate ( ) [2ND] [QUIT] ready to do arithmetic [ ] 2 [ENTER] APR [MODE] Select FLOAT, then 2 [ENTER] set decimal back to 2 places Here s the big picture. Tara gets net proceeds of $5,940, pays $, for 7 years, and must also pay $06,58.8 (the unpaid balance) at the end of 7 years. She is paying 8.35% (the APR) for the use of the money.

9 Example of Unit 9.5 Four years ago, you purchased some corporate stock for $2,000. You received dividends as follows: $00 at the end of year, $50 at the end of year 2, nothing at the end of year 3, and $25 at the end of year 4. Immediately after receiving the final dividend check, you sold the stock for $2,700. What is your annual rate of return? Note: To find an IRR, enter values in this order: Initial cash flow, remaining CF List, and CF Frequencies if more than once: CF0, {CF List}, {CF Freq}. Remember to separate each of the 3 components by a comma. In this problem you received a total of $2,825 in year 4 ($25 dividend + $2,700 sales proceeds). [APPS] [ENTER] : TVM cursor on Choice (TVM) Scroll down to 8: [ENTER] irr( in IRR menu [( )] 2000, irr(-2000, entered initial cash flow (as a negative) [2nd] { 00, 50, 0, 2825 [2nd] } {00, 50, 0, 2825} cash flows entered [ENTER] 2.06 IRR Example 3 of Unit 9.5 (Condensed). Florence Curtis decides to sell her office supply business. Michael Gabriel offers to buy the business by paying $2,000 at the end of each month for 0 years, followed by $3,000 at the end of each month for 5 years. Assuming that money is worth 8.5% compounded monthly (that is the rate that Florence can earn on her money), what is the present value of Michael s offer? Note: To solve for NPV, enter values in this order: periodic interest rate, Initial cash flow, remaining CF List, CF Frequencies: Rate, CF0, {CF List}, {CF Freq}. [APPS] [ENTER] : TVM cursor on Choice (TVM) Scroll down to 7: [ENTER] npv( in NPV menu 8.5 [ ] 2, npv(8.5/2, entered periodic rate 0, npv(8.5/2, 0, initial cash flow of zero entered [2nd] { 2000, 3000 [2nd] }, {2000, 3000}, cash flows entered [2nd] { 20, 60 [2nd] } {20, 60} cash flow frequencies entered [ENTER] 223,994.6 present value of Michael s offer