5 banks offer nominal rates of 6%, but differ in their compounding frequency. A

Question

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.

Explanation / Answer

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 discounting

Details Details A B C D E Nominal Interest Rate 6% Deposit 5000 5000 5000 5000 5000 5000 FVF @6% (1+r)n (1+r)n (1+r)n (1+r)n (1+r)n n=No of compounding periods 1 2 4 12 365 r=Nominal Interest 6%/No of Compounding Period 6%/1 6%/2 6%/4 6%/12 6%/365 6.0000% 3.0000% 1.5000% 0.5000% 0.0164% FVF @ respective interest rate EAR (1+6%)^1 (1+3%)^2 (1+1.5%)^4 (1+.5%)^12 (1+.016%)^365 1.06 1.0609 1.06136355 1.06167781 1.06183131 EAR FVF -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 1 With Compounding Deposit*FVF 5,300.00 5,304.50        5,306.82        5,308.39        5,309.16 FV 2 With out Compounding Deposit*FVF 5,300.00 5,300.00        5,300.00        5,300.00        5,300.00

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