why in below question at part a) for n , write used \'1\' ? I though n is number
ID: 2816839 • Letter: W
Question
why in below question at part a) for n , write used '1' ? I though n is number of years and it should be 2/56 ( 1 year is 56 weeks) in part c, I do not undrestand the question either please solve part c and why in part a we put 1 becasue loaning period was 2 weeks not 1 year, and my third question is in F = P ( 1+i)^n , what kind of interest rate i is? nominal per year or nominal compound or effective?
A payday lender lends money on the following terms: "If I give you $100 today, you will write check for $120, which you will redeem or I will cash on your next payday." Noting that ee me a calculated rates would be even higher for closer paydays, assume that the payday is twow away (a) What nominal interest rate per year (r) is the lender charging? (b) What effective interest rate per year (ia) is the lender charging? (c) If the lender started with $100 and was able to keep it, as well as all the money received, loaned out at all times, how much money does the lender have one year? at the end of 93 Nominal and Effective Interest SOLUTION TO PART a F PF/P, i,n) 120 =: 100(F/P, i I ) Therefore,-20% per 2-week period Nominal interest rte per year 26 0.20 5.20 520%Explanation / Answer
PAYDAY IS EVERY 2 WEEKS
AS THERE ARE 52 WEEKS IN A YEAR, YOU WILL GET PAY 26 TIMES (52 WEEKS/2 WEEKS) IN A YEAR
NOW AS SAID IN SUM, THAT, PAYMENT HAS TO BE MADE ON NEXT PAYDAY, THAT IS 2 WEEKS
AS WE SAID, YOU WILL GET PAY 26 TIMES, THE NEXT PAYDAY IS TO BE TAKEN AS "1" , AS WE HAVE TO FIND NOMINAL RATE PER PERIOD FIRST & THEN ANNUAL.
(THINK YOU ARE TALKING OF 26 YEARS, AND FIRST PAYDAY IS FIRST YEAR)
SO THE FIRST ANSWER, WE ARE GETTING A NOMINAL RATE FOR A SINGLE PERIOD
FV = PV (1+i)n
120 = 100 (1+i)1
THEREFORE i =20% FOR FIRST PAY DAY, THAT IS 2 WEEKS
ANSWER 1 : NOMINAL RATE FOR THE YEAR = 20% X 26 = 520%FOR A YEAR
NOW TO CALCULATE EFFECTIVE RATE
WE WILL USE GIVEN FORMULA, AND AS I SAID YOU WILL GET PAY FOR 26 TIMES, WE HAVE TO TAKE m=26 TO GET EFFECTIVE RATE
I HOPE SECOND IS CLEAR
IN THIRD CASE, RATE IS GIVEN PER PERIOD, THAT IS 20% FOR 2 WEEKS, SO IT IS A NOMINAL RATE WHICH IS USED.
SO 20% RATE IS PER PERIOD THAT IS FOR 2 WEEKS
(SEE GENERALLY WE TAKE n= 1 YEAR, HERE WE TAKE n = 1 PERIOD = 2 WEEKS, SO THERE WILL BE TOTAL 26 PERIODS, SO n =26)
ONE MORE EXAMPLE
WE IF TAKE QUARTERLY CASE, THEN n=4, THOUGH THERE IS ONE YEAR, SAME WAY HERE n=26
(STILL DOUBTS, FEEL FREE TO ASK. THUMBS UP PLEASE)
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