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problems of Ch5.docx - What is the difference in EAR for...

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4 - What is the difference in EAR for two investments A and B, if you know that APR is 8% for both of them, and interest is paid annually for A and quarterly for B ? We should calculate EAR for both A and B as follows EAR A = ( 1 + APR m ) m 1 = ( 1 + 8 1 ) 1 1 = 8 EAR B = ( 1 + APR m ) m 1 = ( 1 + 8 4 ) 4 1 = 8.24 Then the difference is 0.24% EAR B EAR A = 8.24 8 = 0.24 6 . What is the nominal interest rate on an investment that equals $10,000 today and its future value is $28,500 after 10 years, if you know that the interest is paid annually and the expected inflation is 5.5% ? The real interest rate is Real Interest Rate = ( FV PV ) 1 n 1 Real Interest Rate = ( 28500 10000 ) 1 10 1 = 0.11 Then we can get the nominal interest rate as follows Nominal Interest Rate = Real Interest Rate + Expected Inflation Rate Nominal Interest Rate = 11% + 5.5% = 16.5%
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8 . How can you explain the relationship between nominal interest rate and risk- free rate, and default premium and maturity premium ? Risk-free rate is that rate the investor will earn on a loan when the borrower never defaults, like the interest rate on Treasury bills because the government will never default. This risk-free rate, r f , consists of two elements – real interest rate and inflation rate r f = r ¿ + h Where r ¿ is the real interest rate and h is the inflation rate. However, in the case that the borrower defaults, the investor will be compensated by the default premium, dp . In addition, the investor should be compensated for waiting until full repayment has been received, and this is the maturity premium mp . Thus, the nominal interest rate is calculated as the following: r = r ¿ + h + dp + mp 1. Periodic interest rates . In the following table, fill in the
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