# What will be the amount of the annuity assume

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What will be the amount of the annuity (assume interest rate of 7%)? How much will the final payment be worth if inflation is 3, 6, or 9%? Time of retirement will have \$945,000. When converting Not sure of the answer but I think I know how to do the problem, for the first part since the nominal and real interest rates are the same you would just need to calculate the yearly amount you will have to pay. I could not figure out how to calculate the amount of the annuity With inflation rates, you would take the inflation, and calculate the monthly payment with inflation rates (that would be using real plus nominal). Once you get this, you divide the monthly payment by 1 + the inflation rate raised to the number of periods. This will give you the value of the final payment in first year dollars. FORMULA= P= r(PV) / 1 – (1 + r)^-n SO for the first case, the payment will be \$7,472.78 (\$89673.4 annually) 3%: 89673.4 x 1.03^20 = 161960.1353 o final payment will be worth: \$4137.50 in first-year dollars 6%: 89673.4 x 1.06^20 = 287594.74 o \$2330.05 9%: 89673.4 x 1.09^20 = 502566.57 o \$1333.37 B. Read “Duration is a Key to Bond Funds’ Risk” (Item 4.1). The article gives two definitions of duration. Are they correct? Discuss each carefully. Bond that has had its main components broken up One measure of a bond’s life. It’s a math calculation of how long a bond must be held to realize the stated yield, assuming it was bought at face value no matter what the market does For the investor, duration measures a bond’s fund sensitivity to interest rate increases and declines, and can provide and can provide an early warning of danger’s ahead. The book says that duration is “average maturity” of the payments that make up the security. It’s the weighted average of the maturities of the payments, weighting each payment’s maturity by the share of the payment’s present value in the total value of the security.

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Chapter 4: Pricing Securities Promising a single payment: Present value- amount you would give up now for the right to receive it. o A = P (1 + i), where P is the amount put into the bank and I is the annual interest rate Future value- the amount you will receive at the end of the year, A o Can rearrange above equation to be, P = A ÷ P (1 + i) Inverse relationship between future value and present value Multiple Periods and Compounding Compounding- calculation of interest on interest earned already. o A = P(1 + i)(1 + i), so A = p(1 + i)^2. Market yield- price you would earn by buying a security at its market price and holding it to maturity The Compounding Period and the Effective Annual Rate Compounding period- period over which interest is calculated (calculate interest for 1 month, for the second month you count interest including the interest on the interest you earned in the first month) APR (Annual Percentage Rate)- a stated rate of interest from which the period interest rate is calculated. Only good for calculating the periodic rate Periodic Interest rate- interest rate per compounding period o Periodic interest rate = APR / periods per year

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