5 banks offer nominal rates of 6%, but differ in their compounding frequency. A = annually; B =
semiannually; C = quarterly; D = monthly; and E = daily. INOM 6% Deposit $5,000 (i) EAR (ii)
Deposit $5,000. What is FV1? (iii) Deposit $5,000. What is FV2? (2) Would they be equally able
to attract funds? No. People would prefer more compounding to less. (i) What nominal rate
would cause all banks to provide same EAR as Bank A? Each of these nominal rates based on
the frequency of compounding will provide an EAR of 6%. (3) You need $5,000 at the end of the
year. How much do you need to deposit annually for A, semiannually, for B, etc.. beginning
today, to have $5,000 at the end of the year? (4) Even if the banks provided the same EAR,
would a rational investor be indifferent between the banks? Probably not. An investor would
probably prefer the bank that compounded more frequently.
Solution
Ans
Note 1 Part 1 and 3 sub parts have been answered.
Note 2FV1 & FV2 Could not understand the difference . Has been answered on the assumption
that FV1 and FV2 are future value with and without discountingDetailsDetailsABCDENominal
Interest Rate6%Deposit500050005000500050005000FVF
@6%(1+r)n(1+r)n(1+r)n(1+r)n(1+r)nn=No of compounding periods12412365r=Nominal
Interest6%/No of Compounding
Period6%/16%/26%/46%/126%/3656.0000%3.0000%1.5000%0.5000%0.0164%FVF @
respective interest
rateEAR(1+6%)^1(1+3%)^2(1+1.5%)^4(1+.5%)^12(1+.016%)^3651.061.06091.061363551.061
677811.06183131EARFVF -1 ( Can also be calculated using Excel Funtion
\"Effect\")=Effect(Nominal rate, Compounding period Per
Year)6.00%6.09%6.14%6.17%6.18%FV 1With
CompoundingDeposit*FVF5,300.005,304.50 5,306.82 5,308.39 5,309.16FV 2With
out CompoundingDeposit*FVF5,300.005,300.00 5,300.00 5,300.00 5,300.00
semiannually; C = quarterly; D = monthly; and E = daily. INOM 6% Deposit $5,000 (i) EAR (ii)
Deposit $5,000. What is FV1? (iii) Deposit $5,000. What is FV2? (2) Would they be equally able
to attract funds? No. People would prefer more compounding to less. (i) What nominal rate
would cause all banks to provide same EAR as Bank A? Each of these nominal rates based on
the frequency of compounding will provide an EAR of 6%. (3) You need $5,000 at the end of the
year. How much do you need to deposit annually for A, semiannually, for B, etc.. beginning
today, to have $5,000 at the end of the year? (4) Even if the banks provided the same EAR,
would a rational investor be indifferent between the banks? Probably not. An investor would
probably prefer the bank that compounded more frequently.
Solution
Ans
Note 1 Part 1 and 3 sub parts have been answered.
Note 2FV1 & FV2 Could not understand the difference . Has been answered on the assumption
that FV1 and FV2 are future value with and without discountingDetailsDetailsABCDENominal
Interest Rate6%Deposit500050005000500050005000FVF
@6%(1+r)n(1+r)n(1+r)n(1+r)n(1+r)nn=No of compounding periods12412365r=Nominal
Interest6%/No of Compounding
Period6%/16%/26%/46%/126%/3656.0000%3.0000%1.5000%0.5000%0.0164%FVF @
respective interest
rateEAR(1+6%)^1(1+3%)^2(1+1.5%)^4(1+.5%)^12(1+.016%)^3651.061.06091.061363551.061
677811.06183131EARFVF -1 ( Can also be calculated using Excel Funtion
\"Effect\")=Effect(Nominal rate, Compounding period Per
Year)6.00%6.09%6.14%6.17%6.18%FV 1With
CompoundingDeposit*FVF5,300.005,304.50 5,306.82 5,308.39 5,309.16FV 2With
out CompoundingDeposit*FVF5,300.005,300.00 5,300.00 5,300.00 5,300.00
