Question

3) Effective versus nominal interest rates. Bank A pays 4% interest compounded annually on deposits, Bank B pays 3.75% compounded semiannually, and Bank C pays 3.5% compounded daily. a) Which bank would you use? Why? b) If you deposited $5,000 in each bank today, how much would you have at the end of 2 years? c) What nominal rate would cause Banks B and C to provide the same effective annual rate as Bank A? d) Suppose you do not have $5000 now but need it at the end of 1 year. You plan to make a series of deposits, annually for Bank A, semiannually for Bank B, and daily for Bank C, with payments beginning today. How large must the payments be to each bank?

Answer 1

a No of compounding period oa - Effective Interest Rate = Fit Nominal Int. Rati - Mof compounding period per OR 9. EIR = ( 2 + part 3 - 1 in - Year 1 anuali Given: Bank A IR=4% compounded annually No of periods of compounding in 1 year = n=1 and r=1R=4.1. m'=1 (EBR), = (1 + 47)-1 = 41. BANK B, Interest rate, IR = 3.75y. compounded semina ... Nod periods of compounding in a year = 2 2 and wante za = 3:17= 1.875"). (EIR)3= (1 + 1.8754). - 1 -(1.01875)? 1 = 0.03785 3.7857. BANK C, IR 2 3.5%. compounded daily. m= 365 n'=355 (EIR)- (1 + 3.5°/ -1 – 0.0356 = 3.56%. A) AS bank A has highest effective inteest sate of 44., would invest in bank A . (b) Principal = $5,000 , N=2 years Bank A, future value = 5000 (1+4%) = $5,200 I often year 1. Fuyear 2 = 5200 (1+47.) = $5,408 BANK B, you can calculate for each period or use formula . FV=P(1+ "1. = 3.75% (“ ñ - me 4 nia8 P = 5000 (1+ 3,75%) 8-1 = $ 5,385.68 365 365

365 BANKC, EV=P(1+1)-1 r= 3.5". n. 365X2 = 730 = $ 5000 (1+ 3,5%)*5 -1 = $ 5362.52 c) What nominal rate would cause Bank B & C to provide same Effective Annual rate ( EARD total compoundy formuler, periods EAR= (t Nominal rate per year compounds ) -1 P pevocht EAR=1 m2 n'= 2 2 EAR= (1+ 2 meter for Bank B, 4y = 0.04 = (it to ) - 1 =[1104)"? - 1]x2 = 0.0395 = 3.96"), for Bank e. - 365 41. = 0.04 = (1 + r) - 1 re= [1104) 73651] *365 20.03922 365 20.039 22 . (fr) = 3-922% d) for bank Aten Future value = $ 5000 No a disposits = 1 , Present Investment = ? PV x (1+4%) = $ 5000 ... Investment required in the begining of year PV = $ 5000/1.04 - $ 48070697 for bank B suppose semi-annual cash flow, cara Use formula un excel as = PMI (rate, npei, pv. [fr],[type]] Dores SurfestD365,84 stroke] = PMT [ 3.927 , 2,0, 5000, 1] for Bank a = $2427.43 semiannually = PM TC 3.222%, 365,0, 5000, 17 = $13.43 Nare i use value of [type] =1 for begining of the period 2 . f daily