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141-5-1-514 - Section 5.1 Simple Interest and Compound...

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Unformatted text preview: Section 5.1: Simple Interest. and Compound interest Definition: If the principal. P, is invested fer a time period of t at a simple interest rate of r% (for that period) then the interest earned at the end of the time period is given by [1: Prt The future. value.A or F of the investment at the end of the period is A=P+I=P{1+-rt} : P J- Prt' III—A) Example: Yen invest $500 at an annual simple intemgt rate of 4% fer 6 years. How much interest did yen earn? ‘What is the balance at the end? 1:5 Fri: a", 3",“9‘ :1 5710613430.): 9,7,, Example: You invest $1000 at a menthlv simEle interest rate of 6.5% forg— years. How much interest. did you earn? “That. is the balance at the. end? B 2'40”- I: p» (.05.?) (24) S’IS'LO f} 1,- [0(1fr‘t3 A": [no HM = 251° Example: You invest $2000 for 8 months smei at the. e116: of this time period you have earned $400 of interest. “That is the. 31111113.] simple interest rate? mentth simple interest rate? 5..th Ir—l’rl' 1', PM: (#012000er a» tamer“) r: 1:.— L’” c ('1: ‘3 Definition: Suppose the principal. P1 is invested for 3 years at :1 annual i11- terest. rate of 7% and interest is compounded m times per year. The future # amount, A or F, is given by A = P{1+i}“ = P (1+%)mf Example: Find the balance of the account. if you invest. $600 for T years at. a nominal rate of 5% compounded 1") A} annually. A: :9?) r. 2‘ B} eemiannually. ’05- 7 z 7. 78 I}: and H ’7? C) quarterly. 4' 7 p 99 :2: C 87,1“) 8- a {H .1, D) monthly. ' 0" ’2’7 ! z — 0° ’ — ‘ 'DS' 7 Ejdaily. H ; Lw(;.}§—; : {$1311 Example: You want $2000 in an account at. the end of 3 years. If the account gets a nominal rate of 5.75% compounded quarterly, how much do you start the account with? A-P( m9)“ . 5" 20m) : P( ’4' 3’1' E94 l1 PJnu’.” Examplc: You have thc choice of investing money in one of two different accounts. The. first account. is at Bank A and has a rate of 6.51% compounded sennannualljr. The second account is at Bank B and has a rate of 6.08% compounded daily. “Finch account is thc better deal? A {S Definition: For compound intcrcst, the. offcotivc yield, T'Eff. is given by re“: 'W(”£) "a, e’C‘HG") Example: You invest $2000 in an account that. pays interest compounded monthly. W'hat interest. rate do you need to have a balance of $5,000 at. the 0nd of 3 years. 'I‘VNI Solver The TVM solver that is built function on the TI—33f34 calculators. If you are llHillg the old Tl-83 pram and then per ENTER . oth- cna'iac press the and The sole-ct thc Finance application and prcaa cntcr. Hcrc are the variables that arc used in tho TVM Solver. N: m a: t which is the total nunihcr of periods {conipoundingfil for the life of thc account. 1%: The interest rate per year as a pcrccntagc. PV: The present. \'all|c{.~ata|‘t.il]g value} of [I]? account. FRIT: This is the payment that is math each period. FV: Tho futurc valur-[cnrl valuc] of thr- acmunt. PXY = The numth of ])fl)’l‘ll(‘lll5 pcr roar. C/Y = The number of colnpoundings pcl‘ fi'car. For thiH claw. P1”? and CIT arc cqual am] PMIT:END BEGIN should he Hflt to END. )' — may”; V0 0 ...
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