You deposit $13,000 annually into a life insurance fund for the next 10 years, a

Question

You deposit $13,000 annually into a life insurance fund for the next 10 years, after which time you plan to retire a. If the deposits are made at the beginning of the year and earn an interest rate of 6 percent, what will be the amount in the retirement fund at the end of year 10? (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16)) Future value $181631.3 b. Instead of a lump sum, you wish to receive annuities for the next 20 years (years 11 through 30). What is the constant annual payment you expect to receive at the beginning of each year if you assume an interest rate of 6 percent during the distribution period? Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16)) Annual payment $ 14939.10 c. Repeat parts (a) and (b) above assuming earning rates of 5 percent and 7 percent during the deposit period and earning rates of 5 percent and 7 percent during the distribution period. (Do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16)) Deposit Period Value at 10 Years Annual payment Distribution Period 5 percent 7 percent 5 percent 5 percent 7 percent 7 percent

Explanation / Answer

a) The amount in the fund at the end of the year 10 is the FV of the annuity due of $13000, for 10 years at 6%. Using the formula for FV of annuity due FV = 13000*1.06*(1.06^10-1)/0.06 = $     181,631.35 b) The amount to be received annually for 20 years is an annuity due whose PV = $181,631.35 The annuity amount at 6% = 181631.35*0.06*1.06^20/((1.06*(1.06^20-1)) = $       14,939.10 C) Deposit period interest 5%: Value at 10 years = 13000*1.05*(1.05^10-1)/0.05 = $     171,688.23 Distribution period interest 5%, Annuity payment = 171688.23*0.05*1.05^20/((1.05*(1.05^20-1)) = $       13,120.67 Distribution period interest 7%, Annuity payment = 171688.23*0.07*1.07^20/((1.07*(1.07^20-1)) = $       15,145.94 Deposit period interest 7%: Value at 10 years = 13000*1.07*(1.07^10-1)/0.07 = $     192,186.79 Distribution period interest 5%, Annuity payment = 192186.79*0.05*1.05^20/((1.05*(1.05^20-1)) = $       14,687.21 Distribution period interest 7%, Annuity payment = 192186.79*0.07*1.07^20/((1.07*(1.07^20-1)) = $       16,954.27

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